Question

Find the measure of the numbered angles in the rhombus. The diagram is not drawn to scale.

choices;
A. m < 1 = 90, m < 2 = 76, and m < 3 = 14
B. m < 1 = 90, m < 2 = 14, and m < 3 = 83
C. m < 1 = 90, m < 2 = 14, and m < 3 = 76
D. m < 1 = 90, m < 2 = 14, and m < 3 = 14

Answer 1

C. m < 1 = 90, m < 2 = 14, and m < 3 = 76 is the measure of the numbered angles in the rhombus. The diagram is not drawn to scale.

Answer 2

Answer:

C. $m\angle 1=90^{\circ}$, $m\angle 2=14^{\circ}$, and $m\angle 3=76^{\circ}$

Step-by-step explanation:

We have been given a rhombus. We are asked to find the angles of our given rhombus.

We know that rhombus is a parallelogram, whose all sides are equal.

Since rhombus is parallelogram, so alternate interior angles will be equal. Therefore, measure of angle 2 is 14 degrees.

The diagonals of rhombus are perpendicular bisector of each other, therefore, measure of angle 1 is 90 degrees.

Since diagonals of rhombus are perpendicular bisector of each other, so they divide rhombus into four congruent triangles.

We can find measure of angle 3 using angle sum property.

$m\angle 3+90^{\circ}+14^{\circ}=180^{\circ}$

$m\angle 3+104^{\circ}=180^{\circ}$

$m\angle 3+104^{\circ}-104^{\circ}=180^{\circ}-104^{\circ}$

$m\angle 3=76^{\circ}$

Therefore, measure of angle 3 is 76 degrees and option C is the correct choice.