Question

for each of the following, show all of your work to answer the question asked. remember, you may want to sketch an image to help visualize what the problem is telling you. 5. if ∠1 is complementary to ∠2, m∠1=(3x + 9)°, and m∠2=(x + 21)°, find the measure of both angles.

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

Given \(m\angle1=(3x + 9)^{\circ}\) and \(m\angle2=(x + 21)^{\circ}\), we substitute into the equation: \((3x + 9)+(x + 21)=90\).

Step3: Combine like - terms

\(3x+x+9 + 21=90\), which simplifies to \(4x+30 = 90\).

Step4: Solve for \(x\)

Subtract 30 from both sides: \(4x=90 - 30\), so \(4x=60\). Then divide both sides by 4: \(x = 15\).

Step5: Find \(m\angle1\)

Substitute \(x = 15\) into the expression for \(m\angle1\): \(m\angle1=3x+9=3\times15 + 9=45+9=54^{\circ}\).

Step6: Find \(m\angle2\)

Substitute \(x = 15\) into the expression for \(m\angle2\): \(m\angle2=x + 21=15+21=36^{\circ}\).

Answer:

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