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Find the measure of the numbered angles in each rhombus

Find The Measure Of The Numbered Angles In Each Rhombus class=

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Answer:

Angle 1 = 22°

Angle 2 = 68°

Angle 3 = 68°

Angle 4 = 90°

Step-by-step explanation:

It is a rhombus by the definition:

A rhombus is a quadrilateral whose all four sides are equal in length and opposite sides are parallel to each other. However, the angles are not equal to 90°.

The properties of rhombus is:

(1) Opposite angles are equal

(2) All sides are equal and, opposite sides are parallel to each other

(3) Diagonals bisect each other perpendicularly

(4) Sum of any two adjacent angles is 180°

By property (3):

Angle 4 = 90°

By (1) and properties of isosceles triangle in the top right triangle:

Angle 2 = Angle 3 = 68°

In the top triangle:

Angle 1 + Angle 2 + 90° = 180° (Angle sum of triangle)

Angle 1 = 22°

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