Question

In a triangle PQR , angle Q=3angleR=2(angle P + angleR), then find the value of angleQ​

Answer 1

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✪QUESTION✪:-

In a triangle PQR , angle Q=3angleR=2(angle P + angleR), then find the value of aangleQ

✪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°