Question

Find the measurements of the numbered angles in the rhombus QRST

Answer 1

In a rhombus, the diagonals intersect at an angle of 90º.

Let O be the intersection of both diagonals.

Since the diagonals on a parallelogram intersect at the middle point, and all the sides of a rhombus have the same meaure, then all the triangles that are formed (ROS, TOS, TOQ, ROQ) are congruent.

Then, we know that:

`m\angle1=90º`
`m\angle2=40º`

Since the angles 3 and 2 are complementary angles, then:

`m\angle3=50º`

Since the angles 4 and 3 are congruent, then:

`m\angle4=50º`

Therefore:

`\begin{gathered} m\angle1=90º \\ m\angle2=40º \\ m\angle3=50º \\ m\angle4=50º \end{gathered}`