Question

In triangle PQR , if angle p - angle q = 42 degree and angle q - angle r = 21 degree find angle p angle q and angle r

Answer 1

Answer:

$\angle P = 95\degree,\\</p><p></p><p>\angle Q = 53\degree \: and \\\angle R = 32$

Step-by-step explanation:

Given in ∆PQR ,

$\angle P - \angle Q = 42 \degree\:---(1)$

and

$\angle Q - \angle R = 21 \degree\:---(2)$

/* Subtract equations (2) from (1) , we get

$\angle P - 2 \angle Q + \angle R = 21$

$\implies 2\angle Q +21= \angle P + \angle R\: --(3)$

$But , \angle P + \angle Q +\angle R = 180\degree$

/* Angle sum property */

$\implies (\angle P + \angle R) +\angle Q = 180\degree$

$\implies 2\angle Q+21 + \angle Q = 180\degree$

/* From (3) */

$\implies 3\angle Q = 180-21=159$

$\implies \angle Q = \frac{159}{3}= 53 \degree$

$Substitute \: \angle Q = 53\degree \: in \\</p><p>equation \: (1) \: and \: (2) \:, we \:get$

$\angle P - 53\degree = 42$

$\angle P = 42 + 53 = 95\degree$

and

$53\degree - \angle R = 21$

$\implies -\angle R = 21 - 53 = -32$

$\implies \angle R = 32\degree$

Therefore,

$\angle P = 95\degree,\\</p><p></p><p>\angle Q = 53\degree \: and \\\angle R = 32$

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