Question

(GEOMETRY) Give the name that best describes the parallelogram, and find the measures of the numbered angles. The diagram is not drawn to scale. (image attached)thank you ! :)

Answer 1

If two adjacent sides of a parallelogram are equal in length, then it will be a rhombus because all sides of it will be equal

From the given picture we can see a parallelogram with 4 equal sides, then

The best name describes it is a rhombus

In the rhombus

Every 2 adjacent angles are supplementary (their sum = 180 degrees)

Then the angle that measures 116 degrees and angles 1 and 2 are supplementary because they are adjacent angles

$\angle1+\angle2+116=180$

Subtract 116 from both sides

$\begin{gathered} \angle1+\angle2+116-116=180-116 \\ \angle1+\angle2=64 \end{gathered}$

Since the diagonal of the rhombus bisects the vertices' angles

Since the opposite angles in the rhombus are equal in measure, then

$\angle1=\angle2=\angle3=\angle4$

Divide the sum of <1 and <2 by 2 to find the measure of each angle

$\angle1=\angle2=\frac{64}{2}=32^{\circ}$

The measure of the numbered angles is 32 degrees