Question

in the figure shown, $m\angle 1 = 5x - 9$ and $m\angle 2 = 2x - 6$.

find the measures of $\angle 1$ and $\angle 2$.

$m\angle 1 = \square$

$m\angle 2 = \square$

Explanation:

Step1: Identify angle relationship

From the figure, ∠1 and ∠2 are complementary (since there's a right angle involved, their sum is \(90^\circ\)). So, \(m\angle1 + m\angle2 = 90^\circ\). Substitute the given expressions: \((5x - 9)+(2x - 6)=90\).

Step2: Solve for \(x\)

Combine like terms: \(5x + 2x - 9 - 6 = 90\) → \(7x - 15 = 90\). Add 15 to both sides: \(7x = 90 + 15 = 105\). Divide by 7: \(x=\frac{105}{7}=15\).

Step3: Find \(m\angle1\)

Substitute \(x = 15\) into \(m\angle1 = 5x - 9\): \(5(15)-9 = 75 - 9 = 66\).

Step4: Find \(m\angle2\)

Substitute \(x = 15\) into \(m\angle2 = 2x - 6\): \(2(15)-6 = 30 - 6 = 24\).

Answer:

\(m\angle1 = 66^\circ\)
\(m\angle2 = 24^\circ\)