Question

Find the measures of the numbered angles in rhombus ABCD

Answer 1

Answer:

The answer is

$m < 1 = 90 \\ m < 2 = 53 \\ m < 3 = 53 \\ m < 4 = 37$

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Answer 2

The measures of the numbered angles in the rhombus ABCD are as follows:

m∠1 = 90°

m∠2 = 53°

m∠3 = 53°

m∠4 = 37°

The diagonal AC is perpendicular to the diagonal DB. Therefore,

m∠1 = 90°

The diagonal divide the angles into 2 equal parts. Therefore,

m∠2 = m∠3

opposite angles are equal. Therefore

∠A = ∠C

m∠2  = 53°

m∠3  = 53°

∠D = ∠B

sum of angles in a quadrilateral = 360°

360 -  212 = 148°

∠D = ∠B

148 / 2 = 74

∠D = ∠B = 74°

Therefore,

m∠4 = 1 / 2 ∠D

m∠4 = 1 /2 × 74

m∠4 = 37°

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