Answer: Information given below…
Explanation:
We are given two angle measurements…
72° and 90°
Both triangles are isosceles, meaning that they have two of the same angle measurements. With this information we can figure out the triangle with the two highlighted angles.
The Triangle Sum Theorem states that the sum of the three interior angles of any triangle will always add up to 180°.
180° - 72° = 108°
We’ll divide our answer in half because the triangle is isosceles (two of the same angle measurements).
108° / 2 = 54°
The two highlighted angles on the bottom of the figure each equal 54°.
Now we move to the second triangle. We can use the information above to help us.
90° is one of our three angles.
Remember when we found 54°? We’ll use the 90° angle shown in the diagram and subtract by 54° to get our answer.
90° - 54° = 36°
72° + __ = 180°
This is called a supplementary angle. We need to fill in the blank to finish the equation.
72° + _108°_ = 180°
Now to find x.
We figured ou the other two angle measurements.
36° + 108° + __ = 180°
Add these up…
36° + 108° + _36°_ = 180°