Question

$\angle 1$ and $\angle 2$ are complementary angles. if $m\angle 1 = (4x + 30)\degree$ and $m\angle 2 = (x - 5)\degree$, then find the measure of $\angle 2$.

Explanation:

Step1: Define complementary angles

Complementary angles sum to $90^\circ$, so:
$$(4x + 30) + (x - 5) = 90$$

Step2: Simplify the equation

Combine like terms:
$$5x + 25 = 90$$

Step3: Solve for $x$

Subtract 25, then divide by 5:
$$5x = 65 \implies x = 13$$

Step4: Calculate $m\angle2$

Substitute $x=13$ into $\angle2$'s expression:
$$m\angle2 = 13 - 5$$

Answer:

$8^\circ$