Question

1. converse: (5x)° 87° (10x + 17)° m

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. The angle with measure $(5x)^{\circ}$ and the angle adjacent to the $(10x + 17)^{\circ}$ angle (which is $180-(10x + 17)=(163 - 10x)^{\circ}$) are vertical angles. So, $5x=163 - 10x$.

Step2: Solve the equation for x

Add $10x$ to both sides of the equation $5x=163 - 10x$. We get $5x+10x=163$, which simplifies to $15x = 163$. Then $x=\frac{163}{15}\approx10.87$. But if we assume the $(5x)^{\circ}$ and $(10x + 17)^{\circ}$ angles are supplementary (since they seem to be on a straight - line in the context of the intersection of lines), we have $5x+(10x + 17)=180$.

Step3: Solve the new equation for x

Combine like terms: $5x+10x+17 = 180$, so $15x+17 = 180$. Subtract 17 from both sides: $15x=180 - 17=163$. Then $x = 11$.

Answer:

$x = 11$