Question

19 given ∠1 and ∠2 are a linear - pair. • m∠1=x - 15 • m∠2=x + 77 find the measure of each angle. a m∠1 = 49°, m∠2 = 131° b m∠1 = 44°, m∠2 = 136° c m∠1 = 34°, m∠2 = 146° d m∠1 = 50°, m∠2 = 121°

Explanation:

Step1: Recall linear - pair property

Since $\angle1$ and $\angle2$ are a linear pair, $m\angle1 + m\angle2=180^{\circ}$.

Step2: Substitute the given expressions

We have $(x - 15)+(x + 77)=180$.

Step3: Simplify the left - hand side

Combine like terms: $x-15+x + 77=2x+62$. So, $2x+62 = 180$.

Step4: Solve for $x$

Subtract 62 from both sides: $2x=180 - 62=118$. Then divide by 2: $x=\frac{118}{2}=59$.

Step5: Find $m\angle1$

Substitute $x = 59$ into the expression for $m\angle1$: $m\angle1=x - 15=59-15 = 44^{\circ}$.

Step6: Find $m\angle2$

Substitute $x = 59$ into the expression for $m\angle2$: $m\angle2=x + 77=59+77 = 136^{\circ}$.

Answer:

B. $m\angle1 = 44^{\circ},m\angle2 = 136^{\circ}$