Question

question 4
angles a and b are complementary angles. if angle a is twice as big as angle b, what is the measure of angle a?
120 degrees
180 degrees
60 degrees
30 degrees
question 5
angle a is supplementary to angle b. angle b is 4 times greater than angle a. what is the measure of angle b?
45 degrees
135 degrees
144 degrees
36 degrees

Explanation:

Step1: Recall complementary - angle relationship

Complementary angles sum to 90 degrees. Let angle B be \(x\) degrees. Then angle A is \(2x\) degrees. So \(x + 2x=90\).

Step2: Solve for \(x\)

Combining like - terms, we get \(3x = 90\). Dividing both sides by 3, \(x=\frac{90}{3}=30\). Angle A is \(2x\), so angle A \(=2\times30 = 60\) degrees.

Step3: Recall supplementary - angle relationship

Supplementary angles sum to 180 degrees. Let angle A be \(y\) degrees. Then angle B is \(4y\) degrees. So \(y + 4y=180\).

Step4: Solve for \(y\)

Combining like - terms, we have \(5y = 180\). Dividing both sides by 5, \(y=\frac{180}{5}=36\). Angle B is \(4y\), so angle B \(=4\times36 = 144\) degrees.

Answer:

1. C. 60 degrees
2. C. 144 degrees