Question

If JOSE is a rhombus and the measure of angle ESO is 124, what is the measure of angle EJS?

Answer 1

The angle ∠EJS is bisected by the diagonal JS to form an angle of 62°

Response:

• ∠EJS is 62°

What properties of a rhombus can be used to find ∠EJS = 62?

Properties of a rhombus:

The lengths of the sides of a rhombus are equal

The measure of the opposite angles of a rhombus are equal

The diagonals bisect the interior angles of a rhombus

Given that JOSE is a rhombus, and ∠ESO = 124°, we have;

∠EJO = ∠ESO = 124° opposite angles of a rhombus

∠EJS = ∠OJS definition of bisected angle ∠EJO

∠EJS + ∠OJS = ∠EJO by angle addition

• ∠EJS + ∠OJS = 2×∠EJS = ∠EJO = 124°

$\angle EJS = \dfrac{124^{\circ}}{2} = \mathbf{62^{\circ}}$

• ∠EJS = 62°

Learn more about a rhombus here:

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