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ML Aggarwal Solutions Class 8 Mathematics Solutions for Understanding Quadrilaterals Exercise 13.1 in Chapter 13 - Understanding Quadrilaterals
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A heptagon has three equal angles each of 120 and four equal angles. Find the
size of equal angles.
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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