Question

In the given figure, find all the angles of ABC

Answer 1

As angle EAF and angle BAC are vertically opposite angles they are equal and BAC=40 degrees. Angle ACD is 105 degrees so ACB is equal to 180-105=75 degrees as angle ACD and ACB form a linear pair. By angle sum property angles A, B and C sum up to 180 degrees. So 40+75+angle B=180degrees. Angle B= 65 degrees

Answer 2

<A = 40 (vertically opposite angle)
<C = <C + <D = 180 (linear pair)
= <C + 105 = 180
= 180 - 105 = 75
<B = <A + <B + <C = 180 (angle sum property)
= 40 + <B + 75 = 180
= 115 + <B = 180
= 180 - 115 = <B
= 65
therefore, angles are
<A = 40
<B = 75
<C = 65