Question

Find the missing angle measures in the given rhombus.

Answer 1

`(1) = 38\°`

`(2) = 90\°`

`(3) = 90\°`

`(4) = 38\°`

Explanation:

The diagonals of a rhombus are perpendicular to each other, so angles (2) and (3) are equal 90°.

To find angle (1), we can use the sum of internal angles in the left triangle with angles 52°, (1), and (2):

`52 + (1) + (2) = 180`

`(1) = 180 - 52 - 90`

`(1) = 38\°`

The diagonals of a rhombus bisects the angles, to the angle next to the angle of 52° is also 52°, then, in the upper triangle, we have:

`52 + (4) + 90 = 180`

`(4) = 38\°`