Question

Find the measure of the numbered angles in each rhombus.

Answer 1

Answer:

∠1 = ∠2 = ∠3 = ∠4 = 28°

Step-by-step explanation:

A rhombus is a parallelogram with congruent sides. As with any parallelogram, the sum of adjacent interior angles is 180°. The figure is symmetrical, so either diagonal is also an angle bisector.

By any of various rules related to parallel lines and/or angle bisectors and/or isosceles trianges, all of the numbered angles are congruent (= α). Each of them is the complement of half the angle measure shown.

... α = (1/2)(180° -124°) = 90° -62° = 28°

Answer 2

The measure of the numbered angles in each rhombus is $28^\circ$ and this can be determined by using the properties of a rhombus.

Given :

A rhombus ABCD whose $\rm \angle C = 124^\circ$.

A rhombus is a quadrilateral whose all the sides are equal, opposite angles are equal, and opposite sides are parallel.

Line BD is the angle bisector and triangle BCD is the isosceles triangle and therefore, all the numbered angles 1, 2, 3, and 4 are equal.

$\angle 1 = \angle 2 = \angle 3 = \angle 4$

$\angle 1 = \angle 2 = \angle 3 = \angle 4 = \dfrac{1}{2}(180^\circ-124^\circ)$

$\angle 1 = \angle 2 = \angle 3 = \angle 4 = \dfrac{1}{2}(56^\circ)$

$\angle 1 = \angle 2 = \angle 3 = \angle 4 = (28^\circ)$

The measure of the numbered angles in each rhombus is $28^\circ$.

For more information, refer to the link given below:

https://brainly.com/question/8476788