Question

Find the measures of X and Y.

Answer 1

m∠X = 100.5°

m∠Y = 100.5°

Explanation:

`\boxed{\begin{minipage}{6.3cm}\underline{Sum of the interior angles of a polygon}\\\\$S=(n-2) * 180^(\circ)$\\\\where:\\ \phantom{ww}$\bullet$ $n$ is the number of sides. \\ \end{minipage}}`

The given polygon has 6 sides.

Therefore, the sum of its interior angles is:

`\implies S = (6 - 2) * 180^(\circ) = 720^(\circ)`

From inspection of the given polygon:

• m∠V = 99°
• m∠Z = 171°
• m∠U = 159°
• m∠W = 90°
• m∠X = m∠Y

Therefore:

`\implies m \angle U + m \angle V + m \angle W + m \angle X + m \angle Y + m \angle Z = 720^(\circ)`

`\implies 159^(\circ) + 99^(\circ) + 90^(\circ) + m \angle X + m∠ \angle Y + 171^(\circ) = 720^(\circ)`

`\implies m \angle X + m \angle Y + 519^(\circ) = 720^(\circ)`

`\implies m \angle X + m \angle Y = 201^(\circ)`

As m∠X is equal to m∠Y:

`\implies m \angle X = m \angle Y = 201^(\circ) / 2 = 100.5^(\circ)`

Answer 2

• m∠X = m∠Y = 100.5°

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Sum of interior angles of a 6-sided polygon is:

• 180°(6 - 2) = 180°*4 = 720°

Both angles ∠X and ∠Y marked as same, let them be x and ∠W is marked as right angle.

The sum is:

• 2x + 90 + 99 + 171 + 159 = 720
• 2x + 519 = 720
• 2x = 201
• x = 100.5

m∠X = m∠Y = 100.5°.