Question

Find the measure of the acute angle in a rhombus if its side makes with the diagonals angles such that one of them is three times larger than the other.

Answer 1

Answer:

Explanation:

A rhombus has 4 angles. Two obtuse that are equal and two acute that are equal. If all of the angles in a rhombus add up to 360°, then one acute and one obtuse must add up to half that: 180°.

The acute to obtuse angle ratio is 1:3. Think of this as four parts. One part acute, three parts obtuse.

180 ÷ 4 = 45

Therefore, The acute angle is 45°, and the obtuse angle is 135°

Answer 2

The acute angle in the rhombus as required is 45 degrees.

What is an acute angle?

An acute angle is an angle that is less than 90 degrees. Given that; we have two congruent angles then;

2(x + y) = 360

To divide right and left hand sides by 2 we have;

x + y = 180

Now y = 3x so;

4x = 180

x = 45 degrees

Hence, the acute angle in the rhombus as required is 45 degrees.

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