Question

in the figure below, (mangle1=(x + 12)^{circ}) and (mangle2 = 5x^{circ}). find the angle measures.

Explanation:

Step1: Observe angle relationship

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

Step2: Combine like terms

$x+5x+12 = 90$
$6x+12=90$

Step3: Isolate the variable term

Subtract 12 from both sides:
$6x=90 - 12$
$6x=78$

Step4: Solve for x

Divide both sides by 6:
$x=\frac{78}{6}=13$

Step5: Find $m\angle1$

Substitute $x = 13$ into the expression for $m\angle1$:
$m\angle1=(x + 12)^{\circ}=(13 + 12)^{\circ}=25^{\circ}$

Step6: Find $m\angle2$

Substitute $x = 13$ into the expression for $m\angle2$:
$m\angle2=5x^{\circ}=5\times13^{\circ}=65^{\circ}$

Answer:

$m\angle1 = 25^{\circ}$
$m\angle2 = 65^{\circ}$