Question

suppose two angles are complementary and one angle, angle a, has a measure of (4x + 42) degrees, and the other angle, angle b, measures (7x + 81) degrees. solve for x, and determine the measures of angle a and angle b. select one of four angle a: 60° angle b: 30° angle a: 117° angle b: 63° angle a: 63° angle b: 117° angle a: 30° angle b: 60°

Explanation:

Step1: Use the property of complementary angles

Complementary angles sum to \(90^{\circ}\). So, \((4x + 42)+(7x + 81)=90\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(4x+7x+42 + 81=90\), which gives \(11x+123 = 90\).

Step3: Solve for \(x\)

Subtract \(123\) from both sides: \(11x=90 - 123\), so \(11x=- 33\). Then divide both sides by \(11\): \(x=\frac{-33}{11}=-3\).

Step4: Calculate the measure of Angle A

Substitute \(x = - 3\) into the expression for Angle A: \(4x+42=4\times(-3)+42=-12 + 42=30^{\circ}\).

Step5: Calculate the measure of Angle B

Substitute \(x=-3\) into the expression for Angle B: \(7x + 81=7\times(-3)+81=-21+81 = 60^{\circ}\).

Answer:

Angle \(A:30^{\circ}\), Angle \(B:60^{\circ}\)