Question

question
∠1 and ∠2 are vertical angles. if (mangle1=(7x - 16)^{circ}) and (mangle2=(4x + 29)^{circ}), then find the measure of ∠1.

Explanation:

Step1: Set up the equation

Since vertical angles are equal, we set $m\angle1 = m\angle2$. So, $7x - 16=4x + 29$.

Step2: Solve for $x$

Subtract $4x$ from both sides: $7x-4x - 16=4x-4x + 29$, which simplifies to $3x-16 = 29$. Then add 16 to both sides: $3x-16 + 16=29 + 16$, getting $3x=45$. Divide both sides by 3: $x = 15$.

Step3: Find the measure of $\angle1$

Substitute $x = 15$ into the expression for $m\angle1$. $m\angle1=(7\times15 - 16)^{\circ}=(105 - 16)^{\circ}=89^{\circ}$.

Answer:

$89^{\circ}$