One of the corners of the rhombus is 114 °. Calculate the degree measures of other angles.

It is known from the condition that one of the angles of the rhombus is equal to 114 °. And we need to find the degree measure of other angles.

We will argue as follows.

The opposite angles of the rhombus are equal to each other. That is, we can immediately say that the second angle will also be equal to 114 °.

Let us recall the theorem on the sum of the angles of a quadrangle. The sum of all the angles of a quadrilateral is 360 °.

Let’s calculate the sum of the remaining two angles equal to:

360 ° – (114 ° + 114 °) = 132 °.

These angles are also opposite and they are equal to each other:

132 °: 2 = 66 °.

Answer: two angles at 114 ° and two at 66 °.