Question

jack 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 - property

In a parallelogram, opposite angles are equal and adjacent angles are supplementary. Also, use the angle - sum property of a triangle ($180^{\circ}$).

Step2: Identify the angle measuring 76°

Looking at the parallelogram $JKLM$, we can see that the angle marked as $76^{\circ}$ is $\angle1$.

Step3: Find the measure of $\angle5$

In $\triangle JML$, we know that the sum of the interior angles of a triangle is $180^{\circ}$. We know one angle in $\triangle JML$ is $25^{\circ}$ and $\angle JML$ and $\angle KLM$ are adjacent angles in the parallelogram. First, find the measure of $\angle KLM$. Since $\angle JKL$ and $\angle JML$ are adjacent angles in the parallelogram, and we know some angles in $\triangle JKL$. In $\triangle JKL$, we can find $\angle JKL$ using the angle - sum property of a triangle. But an easier way is to note that in $\triangle JML$, if we consider the fact that the opposite sides of a parallelogram are parallel, we can use the properties of alternate interior angles and angle - sum of a triangle.
We know that in $\triangle JML$, let's find $\angle5$. The sum of angles in $\triangle JML$ is $180^{\circ}$. We know one angle is $25^{\circ}$ and we can find the third - angle $\angle5$ by subtracting the sum of the other two known angles from $180^{\circ}$. Since the opposite angles of a parallelogram are equal and using the parallel - side properties, we find that $\angle5 = 42^{\circ}$.

Answer:

Part A: A. $\angle1$
Part B: $42$