Question

I need help with this math please. I have tried multiple times

Answer 1

(a)

In the first figure, every side of the triangle has a marking that indicates they all have the same size. The triangle which has all sides with the same length is called an equilateral triangle, and all the angles are also equal.

Because the sum of all the inner angles for any triangle will always sum 180°, we can calculate as it follows:

`\begin{gathered} x+x+x=180\degree\to3x=180\degree \\ x=(180\degree)/(3)=60\degree \end{gathered}`

And from the solution developed above, we conclude the required angle is:

`m\angle M=60\degree`

(b)

In the second figure, it was given that two sides of the triangle have the same length and that the angle they form is equal to 110°. Every time a triangle has two sides equal to each other, the two angles which are opposite to the angle they form have the same size. If we call each one of Y, we can use the above-cited property of any triangle, that the sum of the inner angles will always be 180° to perform the calculation that follows:

`\begin{gathered} y+y+110\degree=180\degree \\ 2y=180\degree-110\degree=70\degree \\ y=(70\degree)/(2) \\ y=35\degree \end{gathered}`

From the solution developed above, we are able to conclude that:

`m\angle Q=35\degree`