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: Identify angle relationship

Since $\angle1$ and $\angle2$ are complementary (as the corner is a right - angle), $m\angle1 + m\angle2=90^{\circ}$.
So, $5x+(x - 12)=90$.

Step2: Simplify the equation

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

Step3: Solve for x

Add 12 to both sides: $6x=90 + 12=102$. Then divide both sides by 6: $x=\frac{102}{6}=17$.

Step4: 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) $m\angle1=85^{\circ}$