Question

In triangle PQR, angle P = ( y+20) degree,angle Q = ( 2y  -10) degree and angle R =(2y -30) degree, find y degree​

Answer 1

Answer:

Given ∠A=(2x−10)∘,∠B=(2y−20)∘,∠C=(2y+30)∘ and ∠D=(3x+10)∘.

We know, the sum of  the opposite  angles of  a  cyclic  quadrilateral  is  180∘.

So ∠A+∠C=180∘

⇒(2x−10+2y+30)∘=180∘

⇒(2x+2y)∘=160∘−−−−−−(1)

&also, ∠B+∠D=180∘

⇒(2y−20+3x+10)∘=180∘

⇒(3x+2y)∘=190∘−−−−−−(2) .

Subtracting (1) from (2), we  get,

(3x−2x)∘=190∘−160∘

⇒x∘=30∘.

Using x∘=

30∘ in (1), we  get,

(2y+2×30)∘=160∘

⇒(2y+60)∘=160∘

⇒(2y)∘=100∘

⇒y∘=50∘.

So, ∠A=(2x−10)∘=(2×30−10)∘=(60−10)∘=50o

∠B=(2y−20)∘=(2×50−20)∘=(100−20)∘=80o

∠C=(2y+30)∘=(2×50+30)∘=(100+30)∘=130o 

and ∠D=(3x+10)∘=(3×30+10)∘=(90+

Step-by-step explanation:

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