In $Δ$ $P Q R$ , an exterior angle at $R$ is represented by $5 x + 10$ . If the two non-adjacent interior angles are represented by $3 x + 15$ and $3 x - 20$ , find the value of the exterior angle, $∠$ $R$ .

90^{o}

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80^{o}

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84^{o}

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85^{o}

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Solution

The correct option is D $85^{o}$
The exterior angle is equal to the sum of the two non-adjacent interior angles.
$3 x + 15 + 3 x - 20 = 5 x + 10$
$6 x - 5 = 5 x + 10$
$6 x - 5 x = 10 + 5$
$x = 15$
Therefore, $∠$ $R = 5 x + 10 => 5 \times 15 + 10 = 85^{o}$

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