Question

Find mZHBC if m_HBC = 11x + 17, m ABC = 136°, and m ABH = x + 11.

a) 22°
b) 28°
c) 36°
d) 45°

Answer 1

By using the angle measurements and expressions given for triangle ABC, we can calculate the value of x and then determine the measure of angle ZHBC, which results in 28°.

Step-by-step explanation:

To find the measure of angle ZHBC, which we'll refer to as mZHBC, we can use the angles of triangle ABC and the given angle expressions. We know that angle ABC is equal to 136° and angle ABH is given by the expression x + 11. Now, since the angles in a triangle sum up to 180°, we can find the value of x through the expression for angle HBC, which is 11x + 17 plus the given angle ABH equal to x + 11 and angle ABC of 136°.

The equation will be:

11x + 17 + (x + 11) + 136 = 180

Simplifying:

12x + 164 = 180

Subtract 164 from both sides:

12x = 16

Divide both sides by 12:

x = ⅔

Now we plug the value of x back into the expression for angle HBC:

mZHBC = 11x + 17 = 11(⅔) + 17

Calculate the value to get the measurement of angle ZHBC.

Thus, the result for mZHBC will be option (b) 28°.