Final answer:
To calculate the measure of angle XYQ, we solve the equation derived from the given expressions for angles XYQ and QYZ that form a straight line: (10a + 2) + (5a - 2) = 180. After solving for a, we find that a = 12. Substituting a into the expression for angle XYQ, we find that m∠XYQ is 122 degrees.
Step-by-step explanation:
To find the measure of angle XYQ (m∠XYQ), we can use the fact that angles XYQ and QYZ form a straight line when they are adjacent and that the sum of angles on a straight line is 180 degrees. The measures of angles XYQ and QYZ are given as (10a+2) degrees and (5a-2) degrees respectively. Therefore, we set up an equation:
(10a + 2) + (5a - 2) = 180
Simplifying the equation, we combine like terms:
10a + 5a + 2 - 2 = 180
15a = 180
Dividing both sides by 15 to solve for a, we find:
a = 180 / 15
a = 12
Now we substitute a back into the expression for the measure of angle XYQ:
m∠XYQ = 10a + 2
m∠XYQ = 10(12) + 2
m∠XYQ = 120 + 2
m∠XYQ = 122 degrees.