Question

1. ∠1 and ∠2 are vertical angles. if m∠1=(17x + 1)° and m∠2=(20x - 14)°, find m∠2

Explanation:

Step1: Recall vertical - angle property

Vertical angles are equal. So, $m\angle1 = m\angle2$.
We set up the equation: $(17x + 1)=(20x-14)$.

Step2: Solve the equation for $x$

First, move the $x$ - terms to one side:
$17x-20x=-14 - 1$.
Combining like - terms gives: $-3x=-15$.
Then, divide both sides by $-3$: $x = 5$.

Step3: Find $m\angle2$

Substitute $x = 5$ into the expression for $m\angle2$.
$m\angle2=(20x-14)$.
$m\angle2=20\times5-14$.
$m\angle2 = 100 - 14$.
$m\angle2 = 86^{\circ}$.

Answer:

$86^{\circ}$