Question

 In the given figure, 'l' is parallel to 'm' and 'a' is a transversal. If angle 3 = 65 degree, find the measure of angle 2, angles 4, angle 7 and angle 8.

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Answer 1

Answer:

<2=115°, <4=115°, <7=65°, <8=115°

Step-by-step explanation:

<3=65°

<3 and <2 are corresponding angles.

<3+<2=180°

65°+<2=180°

<2=115°

and <2 and <4 are vertical opposite angles.

<2=<4=115°

<3 and <7 are alternate interior angles.

<3=<7=65°

<7 and <8 are corresponding angles.

<7+<8=180°

65°+<8=180°

<8=115°

Hence proved.

Answer 2

=> angle 3 is Congruent to angle 7

... (Corresponding angles)

angle 3 = 65°

... (Given)

Therefore angle 7 = 65°

=> angle 2 + angle 3 = 180°

... (angles in a linear pair)

angle 2 + 65° = 180°

angle 2 = 180°-65°

angle 2 = 115°

=> angle 2 is Congruent to angle 4

... (vertically opposite angles)

angle 2 = 115°

Therefore angle 4 = 115°

[ we can also find it by angles in a linear pair by taking angle 3]

=> angle 3 + angle 8 = 180°

... (interior angles)

angle 3 = 65°

65°+ angle 8 = 180°

angle 8 = 180° - 65°

angle 8 = 115°

[ we can also find it by angles in a linear pair by taking angle 7]

[ we can also find it by corresponding angles by taking angle 4]

[ we can also find it by alternate angles by taking 2]

● Hope it helps you.