Question

2. The acute angle below has a degree measurement that is one fifth of the degree measure of the obtuse

Answer 1

Answer:

Acute angle = 30°

Obtuse angle = 150°

Step-by-step explanation:

Method 1:

Let x represent the measurement of the obtuse angle

Obtuse angle = x

Acute angle = ⅕ of x = x/5

Thus:

x + x/5 = 180° (angels on a straight line)

Solve for x

(5x + x)/5 = 180

Multiply both sides by 5

5x + x = 180 × 5

6x = 900

x = 900/6

x = 150

Obtuse angle = 150°

Acute angle = x/5 = 150/5 = 30°

Method 2:

Since acute angle = ⅕ of the obtuse angle, therefore,

Obtuse angle = 5*acute angle

Let acute angle = x

Obtuse angle = 5x

Equation:

5x + x = 180° (angles on a straight line)

Solve for x

6x = 180

x = 180/6

x = 30

Acute angle = x = 30°

Obtuse angle = 5x = 5*30 = 150°