Question

$\overline{\mathrm{GM}}$is a median of right $\Delta \mathrm{IRG}$

If$\mathrm{m}\angle 4=7\mathrm{x}-3$ and $\mathrm{m}\angle 3=6\left(\mathrm{x}+1\right)$find the value of x.

Short answer

The value of x is 9.

Step-by-step solution

Step 1. Description of step.

The length of the median is equal to half the length of the hypotenuse.

Therefore, $MI=MG$.

Step 2. Description of step.

Consider $\Delta GMI$, in which $MI=MG$then by isosceles triangle theorem, $m\angle 3=m\angle 4$.

Step 3. Description of step.

Substitute $7x-3$for $m\angle 4$and $6\left(x+1\right)$for $m\angle 3$into $m\angle 3=m\angle 4$.

$\begin{array}{c}7x-3=6\left(x+1\right)\\ 7x-3=6x+6\\ x=9\end{array}$

Therefore, the value of x is 9.