Question

fi. The four angles of a quadrilateral are 2(x - 10), (x + 30, P the four angles. 8. In Figure 1, find the measure of ZQPR. 9. In Figure 2, the bisectors of ZA and ZB meet at point P. If ZC = 50° B35° and ZD = 100°, find the R measure of ZAPB. Fig. 1 In a quadrilateral, CO and DO are the bisectors of ZC a Prove that ZA + ZB = 2 ZCOD. IADRILATERALS ​

Answer 1

Answer:$\huge\underbrace\bold\red{Answer}$

∠QPS=∠APB (Vertically opposite angles) ---- (1)

Consider, △APB

∠APB+∠A+ ∠B=180

∠APB=180

(∠A+∠B) ----- (2)

From equation (1) & (2),

∠QPS=180

(∠A+∠B) ----- (3)

Similarly, ∠QRS=180

(∠C+∠D) ---- (4)

From (3) &(4),

∠QPS+∠QRS=360

(∠A+∠B+∠C+∠D)

∴ ∠QPS + ∠QRS = 180

Hence, PQRS is a quadrilateral whose opposite angles are supplementary.