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Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset Vaia Explanations$ Math

Student Edition · 227 pages

ISBN: 9780395977279

Chapter 5: Q2 (page 197)

In the following figure, a parallelogram $E F G H$ is given and $m ∠ E F G = 70$ . If $m ∠ E F H = 32$ then find $m ∠ E H F$ .

Short Answer

Expert verified

The measure of $m ∠ E H F = 38^{\circ}$ .

Step by step solution

01

Step 1. Apply the concept of a parallelogram.

In a parallelogram, the consecutive angles are supplementary.

02

Step 2. Check the figure.

Consider the figure.

03

Step 3. Step description.

Since the consecutive angles are supplementary therefore find the value of $m ∠ H E F$ as follows:

$\begin{matrix} m ∠ E F G + m ∠ H E F = 180^{\circ} \\ 70^{\circ} + m ∠ H E F = 180^{\circ} \\ m ∠ H E F = 180^{\circ} - 70^{\circ} \\ m ∠ H E F = 110^{\circ} \end{matrix}$

Now find $m ∠ E H F$ as follows:

$\begin{matrix} m ∠ E H F + m ∠ E F H + m ∠ H E F = 180^{\circ} \\ m ∠ E H F + 32^{\circ} + 110^{\circ} = 180^{\circ} \\ m ∠ E H F = 180^{\circ} - 32^{\circ} - 110^{\circ} \\ m ∠ E H F = 38^{\circ} \end{matrix}$

Therefore, the measure is $m ∠ E H F = 38^{\circ}$ .

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