Segment Addition Postulate
If point M is between points A and B, and AM = 3x - 7, MB = 2x + 12, and AB = 43, what is the value of x?
What is x = 7.6?
An angle measuring 127° is classified as what type of angle?
What is an obtuse angle?
Using three points A, B, and C where B is the vertex, write three different ways to name the angle.
What are ∠ABC, ∠CBA, and ∠B?
If ∠ABC = 95°, ∠ABD = 37°, and point D is in the interior of ∠ABC, find ∠DBC.
What is 58°?
Two angles are supplementary. If one angle is 38° more than the other, find both angles.
What are 71° and 109°?
Points P, Q, and R are collinear with Q between P and R. If PQ = 5y - 8, QR = 3y + 14, and PR = 7y + 2, find the length of QR.
What is 20?
If an angle is 15° less than twice its supplement, what type of angle is it?
What is an acute angle (65°)?
If rays BE and BF are drawn from point B, and point D lies in the interior of ∠EBF, how many different angles can be named using only these four points?
What are ∠ABC, ∠CBA, and ∠B?
Ray BF lies in the interior of ∠ABE. If ∠ABF = 3x + 12, ∠FBE = 5x - 8, and ∠ABE = 112°, find the value of x.
What is x = 13.5?
Vertical angles are formed by intersecting lines. If one vertical angle measures (5x - 18)° and its vertical angle measures (3x + 22)°, find x.
What is x = 20?
On line segment CD, points E and F are positioned such that C-E-F-D. If CE = 2a + 5, EF = a - 3, FD = 3a - 1, and CD = 67, find the value of a and the length of CE.
What is a = 11 and CE = 27?
Two angles are complementary. If one angle is 40° more than twice the other, classify both angles.
What are acute angles (16⅔° and 73⅓°)?
Point P is the vertex of four rays: PA, PB, PC, and PD, arranged in that order around P. Name the angle that is supplementary to ∠APD if all four rays are coplanar.
What is ∠DPA (or the reflex angle ∠APD)?
Three rays BP, BQ, and BR extend from point B. If ∠PBQ = 4y + 15, ∠QBR = 2y - 5, and ∠PBR = 7y - 10, find y and determine if Q lies between P and R.
What is y = 20, and yes, Q lies between P and R?
Two complementary angles have measures in the ratio 7:11. Find the measure of the larger angle.
What is 55°?
Three points X, Y, and Z are collinear. If XY = 4k + 7, YZ = 2k - 5, and XZ = 5k + 8, determine whether Y is between X and Z, and find k.
What is Y is between X and Z, and k = 6?
An angle's measure is represented by (3x + 20)°. If this angle is obtuse and its complement would be (x - 10)°, find the range of possible values for the angle's measure.
What is between 110° and 180°?
Given points M, N, O, P, and Q where O is the vertex and rays extend to each other point, if ∠MON = 30°, ∠NOP = 45°, ∠POQ = 60°, what is the measure of ∠MOQ?
What is 135°?
∠XYZ is divided by rays YA and YB into three angles. If ∠XYA : ∠AYB : ∠BYZ = 2:3:4 and ∠XYZ = 126°, find ∠AYB.
What is 42°?
Lines AB and CD intersect at point E. If ∠AEC = 4y + 32 and ∠BED = 6y + 8, find the measures of all four angles formed.
What are 56°, 124°, 56°, and 124°?
Point B divides segment AC in the ratio 3:5. If AB = 6x - 15 and BC = 10x - 25, find the length of AC.
What is 40?
Three angles form a straight line. The first angle is 20° less than the second, and the third angle is 40° more than the second. Classify each angle.
What are acute (40°), right (60°), and obtuse (80°)?
In the notation ∠RST, if this angle measures 75° and ray SU bisects it, name all angles that measure 37.5°.
What are ∠RSU and ∠UST?
Point M is in the interior of ∠PQR, and point N is in the interior of ∠MQR. If ∠PQM = 2a + 18, ∠MQN = a - 6, ∠NQR = 3a - 12, and ∠PQR = 156°, find the measures of all three component angles.
What are ∠PQM = 44°, ∠MQN = 7°, and ∠NQR = 27°?
Three lines intersect at a point, forming six angles. If the measures of the angles going clockwise are x°, 2x°, (x+30)°, x°, 2x°, and (x+30)°, find the value of x and classify the type of angles formed.
What is x = 45°, forming three pairs of vertical angles measuring 45°, 90°, and 75°?