Question

in a quadrilateral PQRS angle P + angle R =2 (angle Q+angle S) if angle P is equal to 40 degree then find the measure of angleR

Answer 1

We know sum is360, & opposite angles are supplementary.
then
P+R+2(Q+S)=360
R=180-40=120

Answer 2

given -- angle p + angle r = 2( angle q + angle s ) .

angle p = 40 .

To find ----- measure of angle r .

Proof ---- angle p + angle r + 2 (angle q + angle s)=360 .

(total angle sum of a quadrilateral is 360°).

40° + angle r +2 ( angle q + angle s ).

40° + angle r + angle q + angle s = 360°/2.

" " " " =180°

Therefore angle r + angle q + angle s =180°-40°

angle r = 120°