Question

May I please get help with this kind of math please. I have tried several times but I’m just so confused

Answer 1

(a) In this part, we have two information:

- the three angles are congruent (indicated by the same drawing in each"

- one of the sides have length 4.

The only type of triangle that has its three angles congruent are the equilateral triangle. Thus, the triangle showed here have to be equilateral. This also means that its three sides are congruent.

Thus:

`\begin{gathered} HI=GH \\ HI=4 \end{gathered}`

(b) In this case, we know that two sides have the same lengths (thus, they are congruent) and the opposite angle of one of them is 40°.

By definition, a triangle with two congruent sides is called a isosceles triangle.

Another property of the isosceles triangle is that the angles opposite to the congruent sides are also congruent.

This means that:

`m\angle L=m\angle J=40\degree`

It is also known that the sum of the interior angles of a triangle is 180°, that is:

`m\angle L+m\angle J+m\angle K=180\degree`

Thus:

`\begin{gathered} m\angle L+m\angle J+m\angle K=180\degree \\ 40\degree+40\degree+m\angle K=180\degree \\ 80\degree+m\angle K=180\degree \\ m\angle K=180\degree-80\degree \\ m\angle K=100\degree \end{gathered}`