Question

Geometry- Question #14 (sorry to the other tutor who was helping me on this problem. wifi went bad n kicked me out. My bad)

Answer 1

Given:

$\triangle HJK\cong\triangle\text{TRS}$

so, the corresponding angles are congruent

$\begin{gathered} m\angle H=m\angle T \\ 51=6a-3 \end{gathered}$

solve the equation to find (a):

$\begin{gathered} 51+3=6a \\ 54=6a \\ a=\frac{54}{6} \\ a=9 \end{gathered}$

So, the measure of the angle T = 51

The sum of the angles of the triangle TRS = 180

so, the measure of the angle S = 180 - (83+51) = 46

$\begin{gathered} m\angle K=m\angle S=46 \\ 7b-10=46 \end{gathered}$

Solve to find the value of (b):

$\begin{gathered} 7b=46+10 \\ 7b=56 \\ b=\frac{56}{7} \\ b=8 \end{gathered}$

So, the answer will be:

$\begin{gathered} a=9 \\ b=8 \end{gathered}$