Question

XºBDIf mzC = 49, find the values of x and y.

Answer 1

The triangle in the picture has two sides to be equal. This means that the triangle is an isosceles triangle.

The base angles of an isosceles triangle are equal.

This implies that angle C = B = 49 degrees

So both angles B and C are 49 degrees each.

Now let's find angle A

A + B + C = 180 degrees (sum of angles in a triangle)

Then

`\begin{gathered} A+49+49=180 \\ A+98=180 \\ A=180-98 \\ A=82^o \end{gathered}`

The line bisects angle A into two equal triangles, that is angle y and the angle at the other side

This means that

`\begin{gathered} y=(82)/(2) \\ \\ y=41^o \end{gathered}`

Now let's find x.

Angles x, y, and B make up a triangle. This means that

`\begin{gathered} x^o+y^o+B^{}=180 \\ x+41+49=180 \\ x+90=180 \\ x=180-90 \\ x=90^o \end{gathered}`

Therefore, x = 90, and y = 41