Question

question
in $\triangle hij$, $\overline{hj}$ is extended through point $j$ to point $k$, $m\angle jhi = (x + 5)\degree$, $m\angle ijk = (6x + 3)\degree$, and $m\angle hij = (2x + 13)\degree$. find $m\angle jhi$.
answer
attempt 1 out of 2
$m\angle jhi = \square\degree$
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Explanation:

Step1: Identify the exterior angle theorem

In a triangle, an exterior angle is equal to the sum of the two non - adjacent interior angles. Here, $\angle IJK$ is an exterior angle of $\triangle HIJ$, so $m\angle IJK=m\angle JHI + m\angle HIJ$.

Substitute the given angle measures: $(6x + 3)=(x + 5)+(2x+13)$

Step2: Solve the equation for x

Simplify the right - hand side of the equation:
$(x + 5)+(2x + 13)=x+2x+5 + 13=3x+18$

So our equation becomes $6x+3 = 3x + 18$

Subtract $3x$ from both sides: $6x-3x+3=3x-3x + 18$, which simplifies to $3x+3=18$

Subtract 3 from both sides: $3x+3 - 3=18 - 3$, so $3x=15$

Divide both sides by 3: $x=\frac{15}{3}=5$

Step3: Find $m\angle JHI$

We know that $m\angle JHI=(x + 5)^{\circ}$. Substitute $x = 5$ into the expression:

$m\angle JHI=(5 + 5)^{\circ}=10^{\circ}$

Answer:

10