G_Line and Angle_II_8_Lesson 2

Line and Angles Overview

Browse the course units below.

Angle

Types

Alternate

Angle

Corresponding

Angle

Co exterior

Angle

Game

type of Angle

Test 1

BLE 9(a,c)

Test 2

BLE 9(b)

Mooc

Test

Types of angle

जब दुई वटा समानान्तर रेखाहरूलाई तेस्रो रेखा(छेदक) ले काट्छ, त्यस अवस्थामा उत्पन्न हुने केही कोणहरू यसप्रकार छन।

When two parallel lines are intersected by a transversal, some of the resulting angles are as follows

Alternate angle (एकान्तर कोण)

When two parallel lines are intersected by a transversal, the angles formed on the inside/outside of parallel lines and opposite sides of the transversal are called "Alternate angle".

In the figure are "Alternate angle".
There are two types of Alternate angles.

भित्री एकान्तर कोण (Interior Alternate Angles)

समानान्तर रेखाहरूको भित्रपट्टि, छड्के रेखाको दुबै पट्टि बनेको कोणहरू, जस्तै माथिल्लो रेखाको एउटा भित्री कोण र तल्लो रेखाको विपरित पक्षको भित्री कोण लाई भित् एकान्तर कोण (Interior Alternate Angles) भनिन्छ।
These are the angles formed inside the parallel lines on opposite sides of the transversal, such as one interior angle from the upper parallel line and another interior angle from the opposite side of the transversal to lower parallel line. For example
\(\measuredangle BPF\) and \(\measuredangle CQE\)

बाहिरी एकान्तर कोण (Exterior Alternate Angles)

समानान्तर रेखाहरूको बाहिरपट्टि, छड्के रेखाको दुबै पट्टि बनेको कोणहरू, जस्तै माथिल्लो रेखाको एउटा बाहिरी कोण र तल्लो रेखाको विपरित पक्षको बाहिरी कोण, लाई बाहिरी एकान्तर कोण (Exterior Alternate Angles) भनिन्छ।
These are the angles formed outside the parallel lines on opposite sides of the transversal, such as one exterior angle from the upper parallel line and another exterior angle from the opposite side of the transversal to lower parallel line. For example
\(\measuredangle BPE\) and \(\measuredangle CQF\)

Select the Alternate Angles

From the figure given above, select the alternate angle for each on the left.

Angle	Alternate Angle

Find the Alternate Angle

Select the angle that is alternate to the highlighted one.

Bottom Line

Top Bottom Line

Corresponding angle (संगती कोण)

छड्के रेखाहरूको एकैपट्टि रहेको, र समानान्तर रेखाको भित्रि-बाहिरी वा बाहिरी-भित्री स्थानमा रहेका कोणहरू, जस्तै माथिल्लो रेखाको एउटा कोण र तल्लो रेखाको सोही पक्षको अर्को कोण संगती कोण लाई संगती कोण (Corresponding angle) भनिन्छ।
Corresponding angles are the angles that are located on the same side of transversal lines and in corresponding positions, such as one angle from the upper line (outside/inside) and the another angle from the same side of the lower parallel line (inside/outside). For example
\(\measuredangle BPE\) and \(\measuredangle DQE\)
The corresponding angle (संगती कोण) are always equal.

Corresponding Angles Matching: Game

Based on the figure given below, select the corresponding angle for each angle on the left.

Angle	Corresponding Angle

Co-interior angle (क्रमागत भित्रि कोण)

समानान्तर रेखाहरूको एकैपट्टि, र भित्री भागमा रहेका कोणहरू, जस्तै माथिल्लो रेखाको एउटा भित्रि कोण र तल्लो रेखाको सोही पक्षको भित्रि कोण क्रमागत भित्रि कोण हुन्छन्।यि कोणहरू समानान्तर रेखाहरूको भित्रपट्टी हुन्छन्।
Co-interior angles are the angles that are located on the same side but inside the parallel lines, such as one interior angle from the upper parallel line and the another interior angle from the same side of the lower parallel line. These angles are situated within the parallel lines. For example
\(\measuredangle BPF\) and \(\measuredangle DQE\)
The sum of Co-interior angle (क्रमागत भित्रि कोण) is always 180 degree.

Co-exterior angle (क्रमागत बाहिरी कोण)

समानान्तर रेखाहरूको एकैपट्टि, र बाहिरी भागमा रहेका कोणहरू, जस्तै माथिल्लो रेखाको एउटा बाहिरी कोण र तल्लो रेखाको सोही पक्षको बाहिरी कोण क्रमागत बाहिरी कोण हुन्छन्।यि कोणहरू समानान्तर रेखाहरूको बाहिरपट्टी हुन्छन्।
Co-exterior angles are the angles that are located on the same side but outside the parallel lines, such as one exterior angle from the upper parallel line and the another exterior angle from the same side of the lower parallel line. These angles are situated outside the parallel lines. For example
\(\measuredangle BPE\) and \(\measuredangle DQF\)
The sum of Co-exterior angle (क्रमागत बाहिरी कोण) is always 180 degree.

Co-Interior Angles Matching Game

Based on the figure below, select the co-interior angle for each angle on the left.

Angle	Co-Interior Angle

Co-Exterior Angles Matching: Game

Based pn the figure below, select the co-exterior angle for each angle on the left.

Angle	Co-Exterior Angle

Example: Identify angles

Based on the figure, complete the table given below.

Now, measure the following angle.

a	b	c	d	e	f	g	h	w	x	y	z

Now, complete the following table, if applicable.

Angle	voa	corresponding	alternate	co-interior	co-exterior	linear-pair
a
b
c
d
e
f
g
h
w
x
y
z

Example: Alternate angle

Based on the figure given below, complete the table given below.

Figure No.	\(\measuredangle APF\)	\(\measuredangle DQE\)	Remarks
(a)
(b)

Conclusion:

1. दुईवटा समानान्तर रेखाहरूलाई एउटा छेदकले काट्दा बन्ने क्रमागत भित्री कोणहरूको सम्बन्ध कस्तो हुन्छ? What is the relation between the co-interior angles which are formed when a transversal cuts two parallel lines? [1U]
the relation between the co-interior angles is, their sum is always 180 degree.
2. दिइएको चित्रमा \(x\) को मान पत्ता लगाउनुहोस्। Find the value of \(x\) in the given figure. [1U]
Here
\(120^\circ = 4x\)(corresponding angles)
or\(x = 30\)
3. सँगको चित्रमा \(XY//BC\), \(\angle ABC=60^\circ\) र \(\angle CAY=70^\circ\) भए \(x\) को मान पत्ता लगाउनुहोस्। In the adjoining figure, if \(XY//BC\), \(\angle ABC=60^\circ\) and \(\angle CAY=70^\circ\), find the values of \(x\). [2U]
Here
\(\angle CAY = \angle ACB = 70^\circ\) (corresponding angles)
Now
\(x+80+70=189\)
or\(x = 30\) degree
4. दिइएको चित्रमा \(\angle BGH\) र \(\angle GHD\) को सम्बन्ध लेख्नुहोस्। Write the relation between \(\angle BGH\) and \(\angle GHD\) in the given figure.[1K]
The relation between \(\angle BGH\) and \(\angle GHD\) in the given figure is "they are co-interior angle".
5. दिइएको चित्रमा, \(\angle PTS\) को एकान्तर कोण कुन हो? In the given figure, which is the alternate angle of \(\angle PTS\)? [1K]
The alternate angle of \(\angle PTS\) is \(\angle MST\) .
6. चित्रमा, \(\angle RNT\) को संगत कोण कुन हो? \\ In the given figure, which is the corresponding angle of \(\angle RNT\)? [1K]
The corresponding angle of \(\angle RNT\) is \(\angle PMT\) .
7. चित्रमा, \(\angle AGE\) को संगत कोण लेख्नुहोस्। \\ Write down the corresponding angle of \(\angle AGE\) in the given figure. [1K]
The corresponding angle of \(\angle AGE\) is \(\angle CHE\) .
8. चित्रमा, \(\angle OPL\) को एकान्तर कोणहरू के के हुन्?
   What are the alternate angles of \(\angle OPL\) in the given figure? [1K]
The alternate angles of \(\angle OPL\) are \(\angle KLM\) and \(\angle QOW\).
9. चित्रमा, \(\angle CDB\) को मान पत्ता लगाउनुहोस्। \\ In the given figure, find the value of \(\angle CDB\) ?. [2U]
In the figure
\(150^\circ + x=180\) (co-interior angle)
or\(x = 95^\circ\)
The value of \(\angle CDB\) is 95 degree.
10. चित्रमा, \(x+y\) को मान पत्ता लगाउनुहोस्। \\ In the given figure, find the value of \(x+y\). [2U]
In the figure
\(x+y=180\) (co-interior angle)

11. चित्रमा, \(x\) को मान पत्ता लगाउनुहोस्। \\ In the given figure, find the value of \(x\). [1U]
In the figure
\(x=150\) (alternate angle)

12. चित्रमा, रेखाहरू \(XY\) र \(ZW\) समानान्तर छन् वा छैनन्? कारणसहित लेख्नुहोस्। \\ In the given figure, write down with reason whether the lines \(XY\) and \(ZW\) are parallel or not? [2R]
In the figure
The lines \(XY\) and \(ZW\) are parallel because "corresponding angles are equal".
13. चित्रमा, के रेखाहरू \(ST\) र \(PR\) समानान्तर छन् वा छैनन्? कारणसहित लेख्नुहोस्। \\ In the given figure, are the lines \(ST\) and \(PR\) parallel or not? Write down with reason. [2R]
In the figure
The lines \(ST\) and \(PR\) are parallel because "alternate angles are equal".
14. चित्रमा, \(x\) को मान पत्ता लगाउनुहोस्। \\ In the given figure, find the value of \(x\). [1U]
Here
\(150^\circ + x = 180^\circ\) (co-exterior)
or\(x = 50^\circ\)

15. चित्रमा, रेखाहरू \(PQ\) र \(RS\) समानान्तर छन् वा छैनन्? कारणसहित लेख्नुहोस्। \\ In the given figure, determine whether the given pair of lines \(PQ\) and \(RS\) are parallel or not. Give reason. [2R]
In the figure
The lines \(PQ\) र \(RS\) are parallel because "alternate angles are equal".

1. चित्रमा, \(x\) को मान पत्ता लगाउनुहोस्। \\ In the given figure, find the value of \(x\). [1U]
In the figure
\(2x+10=50\) (corresponding angles)
or\(2x = 40^\circ\)
or\(x = 20^\circ\)

2. चित्रमा \(AB||CD\) भए \(x\) को मान पत्ता लगाउनुहोस्। \\ In the figure \(AB||CD\), find the value of \(x\). [2U]
In the figure
\(2x-30=x+10\) (corresponding angles)
or\(2x-x = 40\)
or\(x = 40\)

3. चित्रमा रेखाहरू \(AB||CD\) भए \(x\) को मान कति हुन्छ ? कारणसहित लेख्नुहोस्। \\ In the given figure, if \(AB||CD\), what will be the value of \(x\)? Write with reason. [2R]
In the figure
\(x+10=40-x\) (corresponding angles)
or\(x+x = 40-10\)
or\(2x = 30\)
or\(x = 15\)

4. चित्रबाट, \(x\) को मान पत्ता लगाउनुहोस्। \\ Find the value of \(x\) in the given figure. [2U]
5. चित्रबाट, \(x\) को मान पत्ता लगाउनुहोस्। \\ Find the value of \(x\) in the given figure. [2U]
6. दिइएको चित्रमा, \(x\) र \(y\) को मान निकाल्नुहोस्। \\ Find the values of \(x\) and \(y\) in the adjoining figure. [2U]
7. दिइएको चित्रमा, \(a\) र \(b\) को मान पत्ता लगाउनुहोस्। \\ Find the value of \(a\) and \(b\) in the given figure. [2U]
8. दिइएको चित्रमा, \(x\) को मान पत्ता लगाउनुहोस्। \\ Find the value of \(x\) in the given figure. [2U]
9. दिइएको चित्रमा, \(m\) र \(n\) को मान पत्ता लगाउनुहोस्। \\ Find the values of \(m\), and \(n\) in the given figure. [2U]
10. दिइएको चित्रमा, \(e\) को मान पत्ता लगाउनुहोस्। \\ Find the values of \(e\) in the given figure. [2U]
11. दिइएको चित्रमा, \(x\) को मान पत्ता लगाउनुहोस्। \\ Find the values of \(x\) in the given figure. [2U]
12. दिइएको चित्रमा, \(x,y,z\) को मान पत्ता लगाउनुहोस्। \\ Find the values of \(x,y,z\) in the given figure. [3U]
13. दिइएको चित्रमा, \(AB||CD\) देखाउनुहोस्। \\ Show that \(AB||CD\) in the given figure. [3U]
14. In the given figure, if \(AB \parallel ED\), then find the values of \(x\) and \(y\). [2U]
15. On the basis of given figure, find the values of \(x\), \(y\), and \(z\). [2U]
16. In the given parallelogram \(PQRS\), find the value of \(x\). [2U]