Answer:
To find the measure of angle EBH, we can consider the following steps:
1. Understand the given information:
We are given that the measure of angle EBH is represented by the expression (6x + 12)°, and the measure of angle HBC is represented by the expression (8x - 10)°.
2. Set up an equation:
Since angles EBH and HBC are adjacent angles, their measures should add up to 180° (as they form a straight line).
3. Write the equation:
(6x + 12)° + (8x - 10)° = 180°
4. Simplify the equation:
Combine like terms on the left side of the equation:
14x + 2 = 180
5. Solve for x:
Subtract 2 from both sides of the equation:
14x = 178
Divide both sides by 14:
x = 178 / 14
Simplify:
x = 12.71
6. Find the measure of angle EBH:
Substitute the value of x into the expression for angle EBH:
(6x + 12)°
= (6 * 12.71 + 12)°
= 76.26° + 12°
= 88.26°
Therefore, the measure of angle EBH is approximately 88.26°
Explanation: