Question

$\angle 1$ and $\angle 2$ are complementary angles. if $m\angle 1 = (5x - 11)\degree$ and $m\angle 2 = (5x - 19)\degree$, then find the measure of $\angle 2$.

Explanation:

Step1: Define complementary angles

Complementary angles sum to $90^\circ$.
$$m\angle1 + m\angle2 = 90^\circ$$

Step2: Substitute angle expressions

Replace with given algebraic forms.
$$(5x - 11) + (5x - 19) = 90$$

Step3: Simplify and solve for $x$

Combine like terms and isolate $x$.
$$10x - 30 = 90$$
$$10x = 120$$
$$x = 12$$

Step4: Calculate $m\angle2$

Substitute $x=12$ into $m\angle2$ formula.
$$m\angle2 = 5(12) - 19$$

Answer:

$41^\circ$