P and Q are supplementary angles such that P = 2x – 5 and Q = 3x + 10, then find P and Q.
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Step-by-step explanation:
Given, that P = 2x - 5 and Q = 3x + 10
Also, P and Q are supplementary
So, P + Q = 180°
⇒ ( 2x - 5 ) + ( 3x + 10 ) = 180
⇒ 2x - 5 + 3x + 10 = 180
⇒ 5x + 5 = 180
⇒ 5 ( x + 1 ) = 5 ( 36 )
⇒ x + 1 = 36
⇒ x = 36 - 1
⇒ x = 35°
Now,
P = 2 ( 35 ) - 5 = 70 - 5 = 65°
Q = 3 ( 35 ) + 10 = 105 + 10 = 115°
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