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# Question 14

A heptagon has three equal angles each of 120 and four equal angles. Find the

size of equal angles.

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From the question, it is given that,

A heptagon has three equal angles each of 120

Four equal angles = ?

We know that, Sum of measures of all interior angles of polygons = (2n - 4) × 90

Where, n = 7

Where, n=7 \begin{array}{l} =((2 \times 7)-4) \times 90^{\circ} \\ =(14-4) \times 90^{\circ} \\ =10 \times 90^{\circ} \\ =900^{\circ} \end{array}

Sum of 3 equal angles = 120 + 120 + 120 = 360

Let us assume the sum of four equal angle be 4x,

So, sum of 7 angles of heptagon = 900

Sum of 3 equal angles + Sum of 4 equal angles = 900

360 + 4x = 900

\begin{aligned} &\text { By transposing we get, }\\ &4 x=900^{\circ}-360^{\circ}\\ &4 x=540^{\circ}\\ &x=540^{\circ} / 4\\ &x=134^{\circ} \end{aligned}

Therefore, remaining four equal angle measures 135 each.

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