Question

∠1 and ∠2 are complementary angles. if ( mangle1 = (3x + 27)^circ ) and ( mangle2 = (x + 27)^circ ), then find the measure of ( angle2 ).

Explanation:

Step1: Define complementary angles

Complementary angles sum to $90^\circ$, so:
$$(3x + 27) + (x + 27) = 90$$

Step2: Simplify the equation

Combine like terms:
$$4x + 54 = 90$$

Step3: Solve for $x$

Subtract 54, then divide by 4:
$$4x = 90 - 54 = 36$$
$$x = \frac{36}{4} = 9$$

Step4: Calculate $m\angle2$

Substitute $x=9$ into $\angle2$'s expression:
$$m\angle2 = (9 + 27)^\circ = 36^\circ$$

Answer:

$36^\circ$