Question

use the given information to find the indicated angle measure. given m∠nrq = 78°, find m∠prq.

Explanation:

Step1: Set up equation based on angle - addition

Since $\angle NRQ=\angle NRP+\angle PRQ$, we have $(8x + 7)+(4x - 1)=78$.

Step2: Combine like - terms

Combining the $x$ terms and the constant terms on the left - hand side gives $8x+4x+7 - 1=78$, which simplifies to $12x + 6=78$.

Step3: Solve for $x$

Subtract 6 from both sides: $12x=78 - 6=72$. Then divide both sides by 12: $x=\frac{72}{12}=6$.

Step4: Find $m\angle PRQ$

Substitute $x = 6$ into the expression for $\angle PRQ$. So $m\angle PRQ=(4x - 1)^{\circ}=(4\times6 - 1)^{\circ}=(24 - 1)^{\circ}=23^{\circ}$.

Answer:

$23^{\circ}$