Question

question
∠1 and ∠2 are complementary angles. if (mangle1=(3x + 5)^{circ}) and (mangle2=(2x - 15)^{circ}), then find the measure of ∠2.

Explanation:

Step1: Recall complementary - angle property

Complementary angles add up to 90°. So, \(m\angle1 + m\angle2=90^{\circ}\).
\((3x + 5)+(2x - 15)=90\)

Step2: Simplify the left - hand side of the equation

Combine like terms: \((3x+2x)+(5 - 15)=90\), which gives \(5x-10 = 90\).

Step3: Solve for \(x\)

Add 10 to both sides of the equation: \(5x-10 + 10=90 + 10\), so \(5x=100\). Then divide both sides by 5: \(x=\frac{100}{5}=20\).

Step4: Find the measure of \(\angle2\)

Substitute \(x = 20\) into the expression for \(m\angle2\). \(m\angle2=(2x - 15)^{\circ}\), so \(m\angle2=(2\times20 - 15)^{\circ}=(40 - 15)^{\circ}=25^{\circ}\).

Answer:

\(25^{\circ}\)