Question

In the figure below, what is the value of y?40°80°

Answer 1

In the diagram, there are 3 triangles included in the whole.

One to the left, one to the right and one at the top.

Observe the left triangle, one of the angles measures 40 degrees. The angle vertically opposite that angle also measures 40 degrees (vertically opposite angles are equal). Similarly, observe that one of the angles in the triangle on the right measures 80 degrees, and the angle vertically opposite that also measures 80.

This means the triangle with angle y contains two other angles measuring 40 degrees and 80 degrees. For the triangle with angle y;

`\begin{gathered} \angle y+40+80=180\text{ (angles in a triangle sum up to 180)} \\ \angle y+120=180 \\ \text{Subtract 120 from both sides,} \\ \angle y+120-120=180-120 \\ \angle y=60 \end{gathered}`