Question

question
∠1 and ∠2 are complementary angles. if m∠1=(2x + 20)° and m∠2=(4x + 16)°, then find the measure of ∠1.
answer
attempt 1 out of 2
submit answer
watch video
show examples

Explanation:

Step1: Recall complementary - angle property

Complementary angles add up to 90°. So, \(m\angle1 + m\angle2=90^{\circ}\).

Step2: Substitute the given angle - expressions

Substitute \(m\angle1=(2x + 20)^{\circ}\) and \(m\angle2=(4x + 16)^{\circ}\) into the equation: \((2x + 20)+(4x + 16)=90\).

Step3: Combine like - terms

\(2x+4x+20 + 16=90\), which simplifies to \(6x+36 = 90\).

Step4: Solve for \(x\)

Subtract 36 from both sides: \(6x=90 - 36\), so \(6x=54\). Then divide both sides by 6: \(x = 9\).

Step5: Find \(m\angle1\)

Substitute \(x = 9\) into the expression for \(m\angle1\): \(m\angle1=(2x + 20)^{\circ}=(2\times9+20)^{\circ}=(18 + 20)^{\circ}=38^{\circ}\).

Answer:

\(38\)