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∠1 and ∠2 are complementary angles. if m∠1=(3x + 11)° and m∠2=(x + 19)°, then find the measure of ∠1.
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Explanation:

Step1: Recall complementary - angles property

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

Step2: Substitute the given angle expressions

Substitute \(m\angle1=(3x + 11)^{\circ}\) and \(m\angle2=(x + 19)^{\circ}\) into the equation: \((3x + 11)+(x + 19)=90\).

Step3: Simplify the left - hand side of the equation

Combine like terms: \(3x+x+11 + 19=90\), which gives \(4x+30 = 90\).

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 the measure of \(\angle1\)

Substitute \(x = 15\) into the expression for \(m\angle1\): \(m\angle1=(3\times15 + 11)^{\circ}=(45+11)^{\circ}=56^{\circ}\).

Answer:

\(56\)