Question

ln a Triangle PQR if

angle Q = 3 angle R = 2(angleP + angleR) then value of angle Q

will be

1. 110°

3. 40°

2. 120°

4. 102°​

Answer 1

GIVEN✪:-

∠Q = 3∠R

∠Q = 2(∠P + ∠R)

3∠R = 2(∠P + ∠R)

✪TO FIND✪:-

∠Q

✪ANSWER✪:-

➥ 3∠R = 2(∠P + ∠R) [ from given ]

➥3∠R = 2∠P + 2∠R

➥3∠R - 2∠R = 2∠P

➥∠R = 2∠P ➜(1)

➠∠Q = 3∠R [ from given ]

➠∠Q = 3( 2∠P ) [from (1)]

➠∠Q = 6∠P ➜ (2)

we know that ,

☞sum of all the angles of the triangle = 180°

☞∠P + ∠Q + ∠R = 180°

☞∠P + 6∠P + 2∠P = 180 °[from (1) and (2) ]

☞9∠P = 180°

☞∠P = 180°/9

☞∠P = 20°

(1) ➜∠R = 2∠P = 2(20°) = 40°

(2)➜∠Q =6∠P = 6(20°) = 120°

therefore ,

angles of the triangle are

∠P = 20°

∠Q =120°

∠R = 40°