Question

question
∠1 and ∠2 are complementary angles. if m∠1=(5x - 11)° and m∠2=(6x + 2)°, then find the measure of ∠1.
answer attempt 1 out of 8

Explanation:

Step1: Recall complementary - angle property

Complementary angles sum to 90 degrees. So, \(m\angle1 + m\angle2=90^{\circ}\).

Step2: Substitute angle expressions

Substitute \(m\angle1=(5x - 11)^{\circ}\) and \(m\angle2=(6x + 2)^{\circ}\) into the equation: \((5x - 11)+(6x + 2)=90\).

Step3: Simplify the left - hand side

Combine like terms: \(5x+6x-11 + 2=90\), which simplifies to \(11x-9 = 90\).

Step4: Solve for \(x\)

Add 9 to both sides of the equation: \(11x=90 + 9\), so \(11x=99\). Then divide both sides by 11: \(x=\frac{99}{11}=9\).

Step5: Find \(m\angle1\)

Substitute \(x = 9\) into the expression for \(m\angle1\): \(m\angle1=(5\times9-11)^{\circ}=(45 - 11)^{\circ}=34^{\circ}\).

Answer:

\(34^{\circ}\)