Question

∠1 and ∠2 are complementary angles. if (mangle1=(2x + 5)^{circ}) and (mangle2=(2x + 5)^{circ}), then find the measure of ∠1.

Explanation:

Step1: Recall complementary - angle property

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

Step2: Substitute the given angle - measures

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

Step3: Simplify the left - hand side of the equation

Combine like terms: \(4x+10 = 90\).

Step4: Solve for \(x\)

Subtract 10 from both sides: \(4x=90 - 10=80\). Then divide both sides by 4: \(x = 20\).

Step5: Find the measure of \(\angle1\)

Substitute \(x = 20\) into the expression for \(m\angle1\): \(m\angle1=(2\times20 + 5)^{\circ}=(40 + 5)^{\circ}=45^{\circ}\).

Answer:

\(45^{\circ}\)