Question

1. in the figure, m∠1 = 5x and m∠2=(x - 12). find the missing measures. (1pt)

(a) x = __
(b) m∠1 = __

Explanation:

Step1: Set up equation

Since $\angle1$ and $\angle2$ are complementary (as the angle formed by the two - ray intersection is a right - angle, so $m\angle1 + m\angle2=90^{\circ}$), we have the equation $5x+(x - 12)=90$.

Step2: Simplify the left - hand side

Combine like terms: $5x+x-12 = 90$, which simplifies to $6x-12 = 90$.

Step3: Isolate the variable term

Add 12 to both sides of the equation: $6x-12 + 12=90 + 12$, resulting in $6x=102$.

Step4: Solve for x

Divide both sides by 6: $x=\frac{102}{6}=17$.

Step5: Find $m\angle1$

Substitute $x = 17$ into the expression for $m\angle1$. Since $m\angle1 = 5x$, then $m\angle1=5\times17 = 85^{\circ}$.

Answer:

(a) $x = 17$
(b) $m\angle1=85$