Question

∠e and ∠f are vertical angles with m∠e = 5x + 10 and m∠f = 7x - 12. what is the value of x? 15 25 11 7 question 3 2 pts suppose △ith≅△apg. which congruency statement is true? it≅ag th≅ag th≅ap ih≅ag

Explanation:

Step1: Set up the equation

Since vertical angles are equal, we set $m\angle E=m\angle F$. So, $5x + 10=7x - 12$.

Step2: Isolate the variable terms

Subtract $5x$ from both sides: $5x+10 - 5x=7x - 12-5x$, which simplifies to $10 = 2x-12$.

Step3: Solve for $x$

Add 12 to both sides: $10 + 12=2x-12 + 12$, getting $22 = 2x$. Then divide both sides by 2: $\frac{22}{2}=\frac{2x}{2}$, so $x = 11$.

For the second - part:
When $\triangle ITH\cong\triangle APG$, corresponding sides are congruent.
The order of the vertices in the congruence statement matters.
$I$ corresponds to $A$, $T$ corresponds to $P$, and $H$ corresponds to $G$.
So, $\overline{TH}\cong\overline{PG}$, $\overline{IT}\cong\overline{AP}$, and $\overline{IH}\cong\overline{AG}$.

Answer:

For the first question: 11
For the second question: $\overline{IH}\cong\overline{AG}$