Questions: In parallelogram EFGH the m angle E=112°. a. Determine the m angle G. Explain your thinking. b. Determine the m angle H. Explain your thinking.

Transcript text: In parallelogram $E F G H$ the $m \angle E=112^{\circ}$. a. Determine the $m \angle G$. Explain your thinking. b. Determine the $m \angle H$. Explain your thinking.

Solution

Solution Steps

Step 1: Find m∠G

In a parallelogram, opposite angles are congruent. Since ∠E and ∠G are opposite angles, m∠G = m∠E. We are given that m∠E = 112°.

Step 2: Find m∠H

In a parallelogram, consecutive angles are supplementary. This means they add up to 180°. Since ∠E and ∠H are consecutive angles, m∠E + m∠H = 180°. We know m∠E = 112°, so 112° + m∠H = 180°. Subtracting 112° from both sides gives m∠H = 68°.