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DA PI dLLIC $\angle U \angle \angle$ $\newline$ point $\newline$ $10$ . The figure below shows three intersecting lines. $\newline$ Which statement best describes all the possible measures for the angle labeled $y^{\circ}$ ? $\newline$ A. The measure of the angle is $x^{\circ}$ , and it is between $0^{\circ}$ and $70^{\circ}$ . $\newline$ B. The measure of the angle is $x^{\circ}$ , and it is between $110^{\circ}$ and $180^{\circ}$ . $\newline$ C. The measure of the angle is $110^{\circ}+x^{\circ}$ , and it is between $0^{\circ}$ and $70^{\circ}$ . $\newline$ D. The measure of the angle is $110^{\circ}+x^{\circ}$ , and it is between $110^{\circ}$ and $180^{\circ}$ .

Full solution

Q. DA PI dLLIC

\angle U \angle \angle

\newline

point

\newline

10

. The figure below shows three intersecting lines.

\newline

Which statement best describes all the possible measures for the angle labeled

y^{\circ}

\newline

A. The measure of the angle is

x^{\circ}

, and it is between

0^{\circ}

and

70^{\circ}

\newline

B. The measure of the angle is

x^{\circ}

, and it is between

110^{\circ}

and

180^{\circ}

\newline

C. The measure of the angle is

110^{\circ}+x^{\circ}

, and it is between

0^{\circ}

and

70^{\circ}

\newline

D. The measure of the angle is

110^{\circ}+x^{\circ}

, and it is between

110^{\circ}

and

180^{\circ}

Identify Relationship: Look at the figure and identify the relationship between the angles. Since the lines intersect, we can use the properties of vertical angles and linear pairs to determine the measure of $y^{(\angle)}$ .
Use Angle Properties: Vertical angles are equal, so if there's an angle opposite to $y^{(\circ)}$ that is $x^{(\circ)}$ , then $y^{(\circ)}$ is also $x^{(\circ)}$ . If $y^{(\circ)}$ is part of a linear pair with an angle measuring $110^{(\circ)}$ , then $y^{(\circ)} = 180^{(\circ)} - 110^{(\circ)} = 70^{(\circ)}$ because angles in a linear pair sum up to $180^{(\circ)}$ .
Determine Measure of $y^{\circ}$ : Since $y^{\circ}$ is equal to $x^{\circ}$ and we know it forms a linear pair with an angle measuring $110^{\circ}$ , $y^{\circ}$ cannot be greater than $70^{\circ}$ . Therefore, $y^{\circ}$ is between $0^{\circ}$ and $70^{\circ}$ .
Check Answer Choices: Now, we need to check the answer choices to see which one correctly describes the measure of $y^{\circ}$ . The measure of $y^{\circ}$ is $x^{\circ}$ , and it is between $0^{\circ}$ and $70^{\circ}$ , so the correct answer is A.