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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.
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
Thevalueof x which isincludedintermsof both theangles∠PRM and ∠NRP is given by: Option D: x = 18What are supplementary angles?Twoangelswhose sum is 180° are calledsupplementary 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 ofsupplementary angles. That means, if supplementary angles are alignedadjacentto each other, their exterior sides will make astraight line.Here, we're specified that:m∠PRM =measureof angle PRM = (7x -11)°m∠NRP = measure ofangleNRP= (4x -7)°They areadjacentandline segmentsMR and RN are forming a straight line MN, so these angles aresupplementary. That means:(7x -11)° + (4x -7)° = 180°Opening the brackets, and solving intermsofmagnitude, we get:Thus, thevalueof x which isincludedintermsof both theangles∠PRM and ∠NRP is given by: Option D: x = 18Learn more aboutsupplementary angleshere:brainly.com/question/2882938...