Question

question
∠1 and ∠2 are complementary angles. if (mangle1=(4x - 30)^{circ}) and (mangle2=(2x - 18)^{circ}), then find the measure of ∠2.
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Explanation:

Step1: Recall complementary - angle property

Complementary angles sum to 90°. So, \(m\angle1 + m\angle2=90^{\circ}\).
Substitute \(m\angle1=(4x - 30)^{\circ}\) and \(m\angle2=(2x - 18)^{\circ}\) into the equation: \((4x - 30)+(2x - 18)=90\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(4x+2x-30 - 18 = 90\), which simplifies to \(6x-48 = 90\).

Step3: Solve for \(x\)

Add 48 to both sides of the equation: \(6x-48 + 48=90 + 48\), so \(6x=138\).
Divide both sides by 6: \(x=\frac{138}{6}=23\).

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

Substitute \(x = 23\) into the expression for \(m\angle2\): \(m\angle2=(2x - 18)^{\circ}\).
\(m\angle2=2\times23-18\).
\(m\angle2 = 46-18\).
\(m\angle2 = 28^{\circ}\).

Answer:

\(28^{\circ}\)