Question

in the figure below, ( mangle 1 = 3x^circ ) and ( mangle 2 = (x + 42)^circ ). find the angle measures.
( mangle 1 = square^circ )
( mangle 2 = square^circ )

Explanation:

Step1: Identify angle relationship

From the figure, $\angle1$ and $\angle2$ are complementary (sum to $90^\circ$). So, $3x + (x + 42) = 90$.

Step2: Solve for \( x \)

Simplify the equation: $4x + 42 = 90$. Subtract 42: $4x = 48$. Divide by 4: $x = 12$.

Step3: Find \( m\angle1 \)

Substitute \( x = 12 \) into \( 3x \): $3(12) = 36^\circ$.

Step4: Find \( m\angle2 \)

Substitute \( x = 12 \) into \( x + 42 \): $12 + 42 = 54^\circ$.

Answer:

\( m\angle1 = 36^\circ \), \( m\angle2 = 54^\circ \)