Question

1. ∠1 and ∠2 are vertical angles. if (mangle1=(17x + 1)^{circ}) and (mangle2=(20x - 14)^{circ}), find (mangle2).

Explanation:

Step1: Set up the equation

Since vertical angles are equal, we set $m\angle1 = m\angle2$. So, $17x + 1=20x - 14$.

Step2: Solve for $x$

Subtract $17x$ from both sides: $1 = 20x-17x - 14$, which simplifies to $1 = 3x - 14$. Then add 14 to both sides: $1+14=3x$, so $15 = 3x$. Divide both sides by 3: $x=\frac{15}{3}=5$.

Step3: Find $m\angle2$

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

Answer:

$86^{\circ}$