Question

1. find ( mangle q ).

Explanation:

Step1: Use the exterior - angle theorem

The exterior - angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles.
So, \(13x=(6x - 10)+87\).

Step2: Simplify the equation

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Subtract \(6x\) from both sides: \(13x-6x=6x + 77-6x\), which gives \(7x = 77\).

Step3: Solve for \(x\)

Divide both sides of the equation \(7x = 77\) by \(7\): \(x=\frac{77}{7}=11\).

Step4: Find \(m\angle Q\)

Since \(m\angle Q=6x - 10\), substitute \(x = 11\) into the expression.
\(m\angle Q=6\times11-10\).

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Answer:

\(m\angle Q = 56^{\circ}\)