Question

Quadrilateral ABCD is a parallelogram. If ∠A=(4x+13) and ∠D=(5x-22), then find the measure of ∠B and ∠C​

Answer 1

If ABCD is a ||gm

so by properties of ||gm ... they are opposite angles .....<A = <D

so,

4x+13 = 5x-22

replace the numerals

13+22=5x-4x

25°=x

so <A = 4 × 25°+ 13 = 100+13 = 113°

<D = 5 × 25°- 22 = 125-22= 113°

so, as we founded <A. and <D

now we have to find <B and <C

<B + <A = 180° (co interior angles)

<B +113°= 180°

<B = 67°

<B= C (by properties of llgm ... they are opposite angles)

<C = 67°

done