Question

use the diagram below for questions 15 - 17. 15. if (mangle1=(7x - 19)^{circ}), and (mangle2=(x + 5)^{circ}), find (mangle2).

Explanation:

Step1: Set up the equation

Since $\angle1$ and $\angle2$ are vertical - angles (assuming from the context of the problem with intersecting lines), they are equal. So we set up the equation $7x - 19=x + 5$.

Step2: Solve for $x$

Subtract $x$ from both sides: $7x-x-19=x - x+5$, which simplifies to $6x-19 = 5$. Then add 19 to both sides: $6x-19 + 19=5 + 19$, giving $6x=24$. Divide both sides by 6: $x=\frac{24}{6}=4$.

Step3: Find $m\angle2$

Substitute $x = 4$ into the expression for $m\angle2$. Since $m\angle2=(x + 5)^{\circ}$, then $m\angle2=(4 + 5)^{\circ}=9^{\circ}$.

Answer:

$9^{\circ}$