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liubo4ka [24]
3 years ago
13

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

Mathematics
2 answers:
Serjik [45]3 years ago
7 0

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.

blsea [12.9K]3 years ago
3 0
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.
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