Question

Tell whether the triangles are similar. Then find the measure of the missing angles.tol46°5858°78°Are the figures similar?(type YES or NO)The measure of angle X =degreesThe measure of angle Y=degrees

Answer 1

We need to find the missing angles x and y in order to see if the given triangles are similar. We can find them by taking into account that the sum of the interior angles add up to 180, that is, for the small triangle, we have

`46+58+x=180`

and for the big one, we have

`58+78+y=180`

In the first case, we get

`\begin{gathered} 104+x=180 \\ \text{then} \\ x=180-104 \\ x=76 \end{gathered}`

and in the second case, we have

`\begin{gathered} \\ 108+y=180 \\ \text{then} \\ y=180-136 \\ y=44 \end{gathered}`

Then, we can note that the only angle which is equal in both triangles is 58. This implies that the triangles are not similar.

In summary, the answers are

- Are the figure similar? NO

- The measuring of angle X = 76 degrees

- The measuring of angle Y = 44 degrees