Question

Choose either Yes or No to tell whether there is an angle of the given measure shown in the diagram.

Answer 1

The addition of all angles in the diagram is equal to 360 degrees. Let's call angle x to the unknown angle. Then, we have:

`\begin{gathered} m\angle x+160\degree+40\degree+65\degree+25\degree=360\degree \\ m\angle x=360\degree-160\degree-40\degree-65\degree-25\degree \\ m\angle x=70\degree \end{gathered}`

Therefore, there is an angle that measures 70°.

Combining the angles of 160°, 40°, and 65°, we get a new angle, let's call it y, that measures:

`\begin{gathered} m\angle y=160\degree+40\degree+65\degree \\ m\angle y=265\degree \end{gathered}`

Therefore, there is an angle that measures 265°.

Combining the angles of 160°, 70°, 25°, and 65°, we get a new angle, let's call it z, that measures:

`\begin{gathered} m\angle z=160\degree+70\degree+25\degree+65\degree \\ m\angle z=320\degree \end{gathered}`

Therefore, there is an angle that measures 320°.

Combining the angles of 25°, and 65°, we get a new angle, let's call it a, that measures:

`\begin{gathered} m\angle a=25\degree+65\degree \\ m\angle a=90\degree \end{gathered}`

Therefore, there is an angle that measures 90°.

On the other hand, there is no combination of angles that add up to 225°