Question

find the measure of ∠ehb. m∠ehb =

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. $\angle EHB$ and $\angle DGA$ are vertical angles. Also, since $EF\parallel CD$, $\angle EHB=\angle DGA$. And $\angle EHB=(2x + 50)^{\circ}$ and $\angle DGA=(3x + 16)^{\circ}$. So we set up the equation $2x+50 = 3x + 16$.

Step2: Solve the equation for $x$

Subtract $2x$ from both sides: $50=x + 16$. Then subtract 16 from both sides: $x=50 - 16=34$.

Step3: Find the measure of $\angle EHB$

Substitute $x = 34$ into the expression for $\angle EHB$. $\angle EHB=2x+50$. So $\angle EHB=2\times34 + 50=68+50 = 118^{\circ}$.

Answer:

$118$