Question

$\angle1$ and $\angle2$ are complementary angles. if $m\angle1=(6x + 29)^{circ}$ and $m\angle2=(3x + 7)^{circ}$, then find the measure of $\angle1$.

Explanation:

Step1: Recall complementary - angle property

Complementary angles add up to 90 degrees. So, $m\angle1 + m\angle2=90^{\circ}$.
Substitute the given expressions: $(6x + 29)+(3x + 7)=90$.

Step2: Combine like - terms

$6x+3x+29 + 7=90$.
$9x+36 = 90$.

Step3: Solve for x

Subtract 36 from both sides: $9x=90 - 36$.
$9x=54$.
Divide both sides by 9: $x=\frac{54}{9}=6$.

Step4: Find the measure of $\angle1$

Substitute $x = 6$ into the expression for $m\angle1$: $m\angle1=6x + 29$.
$m\angle1=6\times6+29$.
$m\angle1=36 + 29$.
$m\angle1=65^{\circ}$.

Answer:

$65^{\circ}$