Question

In the diagram below, line AE and line DF are parallel. If m∠ABG=11xm∠ABG=11x and m∠HCF=10x+9m∠HCF=10x+9, what is m∠ABGm∠ABG?

a) 102°
b) 99°
c) 81°
d) 9°

Answer 1

In this case, the measure of angle ABG is 99°.

The answer is option ⇒b

Step-by-step explanation:

To find the measure of ∠ABG, we can use the fact that ∠ABG and ∠HCF are alternate interior angles formed by two parallel lines. According to the alternate interior angles theorem, these angles are congruent.

1. Set up an equation using the congruence of ∠ABG and ∠HCF:

m∠ABG = m∠HCF

2. Simplify the equation by substituting the given angle measures:

11x = 10x + 9

3. Solve the equation for x by isolating the variable:

11x - 10x = 9

x = 9

4. Substitute the value of x back into the equation to find m∠ABG:

m∠ABG = 11(9) = 99°

Therefore, the measure of ∠ABG is 99°.

In summary, by using the fact that ∠ABG and ∠HCF are alternate interior angles, we can set up an equation and solve for x. Substituting the value of x back into the equation gives us the measure of ∠ABG as 99°.

The answer is option ⇒b