Question

∠b and ∠d are vertical angles m∠b = (2x + 1)° m∠d = (x + 36)°. Find the measure of each angle.

Answer 1

m<b = 71

m<d = 71

Explanation:

Vertical angles = congruence

2x+1=x+36

subtract x

x+1=36

subtract 1

x = 35

PLUG IN

m<b = 2x + 1

2(35) +1

70+1

71

m<d = x+36

35+36

71

Answer 2

m∠b = 71°

m∠d = 71°

Explanation:

Term: Vertical Angles

Definition: Angles that are non-adjacent formed by two intersecting lines. These angles are equal in degrees

Step 1: Solve for the variable

We know from the definition that these two angles are equal. We can use that to solve for x

2x° + 1° = x°+ 36°

x° + 1° = 36°

x° = 35°

Step 2: Solve for the two angles

We now know the value for the variable x, 35°. We can substitute it when solving for each angle

m∠b

• 2x° + 1° = 2(35°) + 1°
• 70° + 1° = 71°

m∠d

• x° + 36° = 35° + 36°
• 71°

Note, we never actually had to solve for each of the two angles. This is because both angles are congruent according to the defintion. If we solve for one, that value is the same for the other.

-Chetan K