Question

zack wants to determine the missing angle measures in parallelogram jklm. part a which angle measures 76°? ∠1 ∠2 ∠3 ∠4 part b what is the measure of ∠5? m∠5 = °

Explanation:

Step1: Recall parallelogram angle - properties

In a parallelogram, opposite angles are equal.

Step2: Identify the angle equal to 76°

In parallelogram $JKLM$, $\angle JML$ and $\angle JKL$ are opposite angles. Given $\angle JML = 76^{\circ}$, and looking at the angles formed by the diagonals, we know that $\angle 1$ is part of $\angle JML$. So the angle that measures $76^{\circ}$ is $\angle 1$.

Step3: Use angle - sum property of a triangle

In $\triangle JML$, we know two angles: one is $76^{\circ}$ and another is $25^{\circ}$. The sum of the interior angles of a triangle is $180^{\circ}$. Let $\angle 5=x$. Then $x + 76^{\circ}+25^{\circ}=180^{\circ}$.

Step4: Solve for $\angle 5$

$x=180^{\circ}-(76^{\circ} + 25^{\circ})=180^{\circ}-101^{\circ}=79^{\circ}$.

Answer:

Part A: A. $\angle 1$
Part B: $79$