Question

1. ( mangle prq = 80^circ ) and ( mangle srp = 82^circ ). find ( mangle srq ).

Explanation:

Step1: Analyze angle relationship

We know that the sum of angles around a point on a straight line or the sum of adjacent angles forming a larger angle. Here, $\angle SRQ$ is composed of $\angle SRP$ and $\angle PRQ$. So we can use the angle addition postulate, which states that if two angles are adjacent, the measure of the larger angle is the sum of the measures of the two smaller angles. So $m\angle SRQ = m\angle SRP + m\angle PRQ$.

Step2: Substitute the given values

We are given that $m\angle PRQ = 80^\circ$ and $m\angle SRP = 82^\circ$. Substituting these values into the formula from Step 1, we get $m\angle SRQ = 82^\circ + 80^\circ$.

Step3: Calculate the sum

Calculating $82 + 80$, we get $162$. So $m\angle SRQ = 162^\circ$.

Answer:

$162^\circ$