Question

what is the measure of angle h? * your answer 117° 108° 130° 66°

Explanation:

Step1: Calculate the sum of interior angles of the polygon

The sum of interior angles of an \(n\) -sided polygon is \((n - 2)\times180^{\circ}\). Here, \(n=7\), so the sum is \((7 - 2)\times180^{\circ}=900^{\circ}\).

Step2: Set up the equation to find \(h\)

Let the three equal angles in the left - hand polygon be \(x\). Since the left - hand polygon has \(5\) sides, and the sum of its interior angles is \((5 - 2)\times180^{\circ}=540^{\circ}\). We know two of its angles are \(117^{\circ}\) and \(108^{\circ}\), and the three equal angles \(x\). So \(3x+117 + 108=540\), \(3x=540-(117 + 108)=315\), \(x = 105^{\circ}\).

Now, using the sum of interior angles of the \(7\) -sided polygon: \(3\times105+117+108+130+66 + 90+h=900\) (the right - hand part has a right - angle, \(90^{\circ}\)).

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Answer:

\(74^{\circ}\)