Question

use the image below to find the requested values. find the measure of ∠frt. what is the value of k? skill code: 1110114

Explanation:

Part 1: Find the measure of $\angle FRT$ and the value of $k$

Step 1: Identify the relationship between angles

Since $YRF$ is a straight line, the sum of $\angle YRT$ and $\angle FRT$ is $180^\circ$ (linear pair of angles). We know $\angle YRT = 45^\circ$ and $\angle FRT=(6k + 165)^\circ$. So, we can write the equation:
$$45+(6k + 165)=180$$

Step 2: Solve for $k$

First, simplify the left - hand side of the equation:
$$45+6k + 165=180$$
$$6k+210 = 180$$
Subtract $210$ from both sides:
$$6k=180 - 210$$
$$6k=- 30$$
Divide both sides by $6$:
$$k=\frac{-30}{6}=- 5$$

Step 3: Find the measure of $\angle FRT$

Substitute $k = - 5$ into the expression for $\angle FRT$:
$$\angle FRT=6k + 165$$
$$\angle FRT=6\times(-5)+165$$
$$\angle FRT=-30 + 165$$
$$\angle FRT = 135^\circ$$

Answer:

for $\angle FRT$:
The measure of $\angle FRT$ is $\boldsymbol{135^\circ}$.