Competition problem — Geometry — Maths Olympiad Prep

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Geometry Difficulty 2.6 Junior Find the answer

What is the value of $x$ if $P Q S$ is a straight line and $\angle P Q R=110^{\circ}$ ?

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

Since $P Q S$ is a straight line and $\angle P Q R=110^{\circ}$ , then $\angle R Q S=180^{\circ}-\angle P Q R=70^{\circ}$ . Since the sum of the angles in $\triangle Q R S$ is $180^{\circ}$ , then $70^{\circ}+(3 x)^{\circ}+(x+14)^{\circ} =180^{\circ}$ . Solving, $4 x =96$ gives $x =24$ .

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