Question

If we know that two angles of one triangle are 112 ° and 39 °, and two angles of another triangle are 39 ° and 29 °, then the two triangles must _____. Select one:a.be equilateralb.be right trianglesc.not be similard.be similar

Answer 1

Firstly, we will find the third angles of both triangles,

The sum of angles in a triangle is 180 degrees.

If we know that two angles of one triangle are 112° and 39°

Let the third angle be x

`\begin{gathered} 112\degree+39\degree+x=180\degree \\ x=180\degree-151\degree=29\degree \\ x=29\degree \end{gathered}`

The third angle is 29 degrees

And two angles of another triangle are 39° and 29°

Let the third angle be y

`\begin{gathered} 39\degree+29\degree+y=180\degree \\ y=180\degree-68\degree=112\degree \\ y=112\degree \end{gathered}`

The third angle is 112 degrees

Two triangles are similar if their corresponding angles are equal.

Since, their corresponding angles are equal

Hence, then the two triangles must be similar (option d)