Question

in the figure below, m∠1=(x + 30)° and m∠2 = 3x°. find the angle measures.

Explanation:

Step1: Note angle - sum property

$\angle1+\angle2 = 90^{\circ}$ (complementary angles).

Step2: Substitute angle expressions

$(x + 30)+3x=90$.

Step3: Combine like - terms

$4x+30 = 90$.

Step4: Solve for x

$4x=90 - 30=60$, so $x = 15$.

Step5: Find $\angle1$ and $\angle2$

$m\angle1=x + 30=15+30 = 45^{\circ}$, $m\angle2=3x=3\times15 = 45^{\circ}$.

Answer:

$m\angle1 = 45^{\circ}$, $m\angle2 = 45^{\circ}$