Question

Line AE and line DF are parallel. If m∠ABG = 12x and m∠HCF = 11x + 9, what is the measure of angle HCF?

Answer 1

Angle HCF is the same measure as angle ABG since they are corresponding angles. Therefore, the measure of angle HCF is 108 degrees.

Step-by-step explanation:

Given that line AE and line DF are parallel, we can use the properties of parallel lines to find the measure of angle HCF. Since line AE and line DF are parallel, angle ABG and angle HCF are corresponding angles. Therefore, they have equal measures. So, we have:

m∠ABG = m∠HCF

Given that m∠ABG = 12x, we can substitute this value into the equation:

12x = 11x + 9

Simplifying the equation, we get:

x = 9

Substituting x = 9 back into the equation for m∠HCF, we get:

m∠HCF = 11(9) + 9 = 99 + 9 = 108

Therefore, the measure of angle HCF is 108 degrees.

Answer 2

To find the measure of angle HCF, the expressions for angles ABG and HCF are set equal since AE and DF are parallel. Solving the equations gives x = 9, and substituting this into the expression 11x + 9 yields angle HCF as 108 degrees.

Step-by-step explanation:

The subject of this question is finding the measure of an angle when two lines are parallel and an equation is given that relates the angles formed by a transversal. To find the measure of angle HCF, we must recognize that if lines AE and DF are parallel, then the corresponding angles ABG and HCF would be equal when a transversal crosses these two lines. Therefore, the equation m∠ABG = 12x will equal m∠HCF = 11x + 9. By setting the two expressions for the angles equal to each other (12x = 11x + 9), we solve for x, then plug this value into the expression for m∠HCF to get the measure of angle HCF.

Solving 12x = 11x + 9 gives us x = 9. Substituting x into the expression for m∠HCF, we get 11x + 9 = 11(9) + 9 = 108 degrees. Therefore, the measure of angle HCF is 108 degrees.