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What is m∠XYQ? A line segment QY intersects another line segment XZ at the point Y to form the angles XYQ and QYZ measuring (10a+2) degrees and (5a-2) degrees respectively. m∠XYQ =

What is m∠XYQ? A line segment QY intersects another line segment XZ at the point Y-example-1
User Jnkb
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2 Answers

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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.

User Marcio Jasinski
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Answer:

Determine the measure, in degrees, ... Score 2: The student had a complete and correct response. ... a conceptual error and did not find the measure of the smallest angle. ... y x is ΔA B C . State and label the coordinates of ΔA B C . [The use of ... Score 1: The student stated and labeled two points correctly.

Step-by-step explanation:

User RememberME
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