Question

5 fill in the blank 1 point if the measure of an angle is 38°, find the measure of its complement. type your answer... 6 fill in the blank 2 points ∠1 and ∠2 form a linear pair. if m∠1=(5x + 9)° and m∠2=(3x + 11)°, find the measure of each angle.

Explanation:

Step1: Recall the definition of complementary angles

Complementary angles add up to 90°. Let the given angle be \(A = 38^{\circ}\), and its complement be \(C\). Then \(A + C=90^{\circ}\).

Step2: Solve for the complement

\(C = 90^{\circ}-A\). Substitute \(A = 38^{\circ}\) into the formula, so \(C=90 - 38=52^{\circ}\).

for question 6:

Step1: Recall the property of linear - pair angles

Linear - pair angles add up to 180°. So \(m\angle1 + m\angle2=180^{\circ}\).

Step2: Substitute the given expressions for the angles

Since \(m\angle1=(5x + 9)^{\circ}\) and \(m\angle2=(3x + 11)^{\circ}\), we have the equation \((5x + 9)+(3x + 11)=180\).

Step3: Simplify the left - hand side of the equation

Combine like terms: \(5x+3x+9 + 11=180\), which simplifies to \(8x+20 = 180\).

Step4: Solve for \(x\)

Subtract 20 from both sides: \(8x=180 - 20=160\). Then divide both sides by 8, so \(x=\frac{160}{8}=20\).

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

Substitute \(x = 20\) into the expression for \(m\angle1\): \(m\angle1=5x + 9=5\times20+9=100 + 9=109^{\circ}\).

Step6: Find the measure of \(\angle2\)

Substitute \(x = 20\) into the expression for \(m\angle2\): \(m\angle2=3x + 11=3\times20+11=60 + 11=71^{\circ}\).

Answer:

52