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Segment MN and Segment PQ intersect at R, as seen in the diagram at the right. Find x, m∠ MRQ, m∠ QRN, m∠ NRP, m∠ PRM.

A) x=10, m
B) x=20, m
C) x=15, m
D) x=18, m

Segment MN and Segment PQ intersect at R, as seen in the diagram at the right. Find x, m∠ MRQ, m∠ QRN, m∠ NRP, m∠ PRM. A) x=10, m B) x=20, m C) x=15, m D) x=18, class=

Answer :

Answer is 18

18 • 7 = 126
126 - 11 = 115
4 • 18 = 72
72 - 7 = 65

115 + 65 = 180

They are supplementary angles, which mean they together equal 180°

The value of x which is included in terms of both the angles ∠PRM and ∠NRP is given by: Option  D: x = 18

What are supplementary angles?

Two angels whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.

Here, we're specified that:

  • m∠PRM = measure of angle PRM = (7x -11)°
  • m∠NRP = measure of angle NRP= (4x -7)°

They are adjacent and line segments MR and RN are forming a straight line MN, so these angles are supplementary. That means:

(7x -11)° +  (4x -7)° = 180°

Opening the brackets, and solving in terms of magnitude, we get:

[tex]7x - 11 + 4x -7 = 180\\11x - 18 = 180\\11x = 180+18 \\\\x = \dfrac{198}{11} = 18[/tex]

Thus, the value of x which is included in terms of both the angles ∠PRM and ∠NRP is given by: Option  D: x = 18

Learn more about supplementary angles here:

https://brainly.com/question/2882938

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