Question

Find the values of the variables and the measure of the angles.

Answer 1

Since ∠GFE is a right triangle, we can conclude:

`\begin{gathered} b+32=90 \\ b=90-32 \\ b=58 \end{gathered}`

the sum of the internal angles of a triangle is 180, therefore, for the triangle GHF:

`\begin{gathered} 55+a+b=180 \\ \text{ Since b=58} \\ 55+a+58=180 \\ a+113=180 \\ a=67 \end{gathered}`

Finally, for the triangle GEF:

`\begin{gathered} a+90+d=180 \\ 67+90+d=180 \\ 157+d=180 \\ d=180-157 \\ d=23 \end{gathered}`