Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Problems climb from one-step measures to multi-step word situations with algebraic expressions. Sketch each figure and label what is given before solving.
Standards: G-CO.A.1 · Level: Grade 10 Geometry
Problem 1 Adding two segments ★★★
Point Q lies between P and R on a line. Find PR.
Problem 2 Finding a midpoint length ★★★
M is the midpoint of RS, and RM = 18.6 centimeters. Find MS and RS.
Problem 3 Complement and supplement ★★★
Find the complement and the supplement of a 37° angle.
Problem 4 Angles in a linear pair ★★★
∠AOB and ∠BOC form a linear pair, and m∠AOB = 118°. Find m∠BOC.
Problem 5 Vertical angles ★★★
Two lines cross at O. ∠POR measures 74°. Find the measure of its vertical angle and of each of the other two angles.
Problem 6 Segment addition with algebra ★★★
B is between A and C, with AB = 3x + 2, BC = 5x − 7 and AC = 51. Find x, AB and BC.
Problem 7 Angle addition with algebra ★★★
Ray OB lies inside ∠AOC. If m∠AOB = (2x + 10)°, m∠BOC = (3x − 8)° and m∠AOC = 112°, find x and both smaller angles.
Problem 8 Angle bisector equation ★★★
Ray OB bisects ∠AOC. If m∠AOB = (4x + 3)° and m∠BOC = (6x − 17)°, find x and m∠AOC.
Problem 9 Midpoint on a number line ★★★
Points D and E are located at −7 and 12 on a number line. Find the coordinate of the midpoint of DE and the length of DE.
Problem 10 A supplement and a complement ★★★
The supplement of an angle measures 25° more than 3 times the angle’s complement. Find the angle.
Problem 11 Vertical angles with algebra ★★★
Two vertical angles measure (5x − 12)° and (3x + 22)°. Find x, the common measure, and the measure of each angle that forms a linear pair with them.
Problem 12 Linear pair with algebra ★★★
Two angles form a linear pair and measure (7x + 9)° and (5x + 15)°. Find both angles.
Problem 13 A right angle split in two ★★★
Line BA is perpendicular to line BD, and ray BC lies inside ∠ABD. If m∠ABC = (2x + 7)° and m∠CBD = (3x − 2)°, find both angles.
Problem 14 Always, sometimes or never ★★★
Decide whether each statement is always, sometimes or never true. Justify each answer in one sentence.
- Two lines in the same plane that do not intersect are parallel.
- Three points are collinear.
- A ray has a midpoint.
- Two vertical angles are supplementary.
Problem 15 Hiking trail midpoint ★★★
On a straight trail, the trailhead T, a lookout L and a campsite C appear in that order. TL = 2.4 miles and LC = 1.75 miles. A water fountain W sits at the midpoint of TC. Find TC, then find how far the fountain is from the lookout and say which side of the lookout it is on.
Problem 16 Robot sensor beam ★★★
Two walls meet at corner O and form ∠AOC = 128°. A robot at O aims a sensor along ray OB, which bisects ∠AOC. It then turns toward the wall OC and stops at ray OD, where m∠BOD = 19°. Find m∠AOB and m∠DOC.
Problem 17 Four collinear points ★★★
Points A, B, C and D lie on a line in that order. AB = x, BC = 2x − 4, CD = x + 10 and AD = 62. Point M is the midpoint of AD. Find x and each segment length, and state whether M lies between B and C.
Problem 18 Linear pair, vertical angles, bisector ★★★
Two lines cross at O. ∠1 = (3x + 5)° and its neighbor ∠2 = (2x + 15)° form a linear pair. ∠3 is vertical to ∠1 and ∠4 is vertical to ∠2. Find all four angles. Then find the measure of each piece when a ray bisects ∠2.
Problem 19 Highway mile markers ★★★
Exit 1 is at mile marker 14.6 and Exit 2 is at mile marker 31.2 on a straight highway. A rest stop is exactly halfway between the exits. A gas station is 3.5 miles past the rest stop toward Exit 2. Find the mile marker of the rest stop and the distance from the gas station to Exit 2.
Problem 20 Bisector on a straight angle ★★★
Points A, O and D lie on a line. Ray OC bisects ∠BOD. If m∠AOB = (4x − 6)° and m∠BOC = (x + 18)°, find x and all three angles.
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