These twenty-four problems practice Common Core standard 8.G.A.5. Find missing angles in triangles, use the exterior angle theorem, work with angles formed when parallel lines are cut by a transversal, and use the AA criterion to decide whether triangles are similar.
The problems run from one-step angle sums to equations with variables and word problems. Work from easiest to hardest and check each angle set against 180 degrees.
Problem 1: Find the third angle
Two angles of a triangle measure \(48^{\circ}\) and \(67^{\circ}\). Find the third angle.
Problem 2: Right triangle angles
A right triangle has one acute angle of \(35^{\circ}\). Find the other acute angle.
Problem 3: Isosceles triangle
An isosceles triangle has a \(40^{\circ}\) angle between its two equal sides. Find the two base angles.
Problem 4: Angles in a ratio
The angles of a triangle measure \(x^{\circ}\), \(2x^{\circ}\) and \(3x^{\circ}\). Find \(x\) and all three angles.
Problem 5: Exterior angle
Find the exterior angle \(x\) at \(B\).
Problem 6: Missing remote angle
An exterior angle of a triangle measures \(130^{\circ}\). One remote interior angle measures \(80^{\circ}\). Find the other remote interior angle.
Problem 7: Corresponding angles
Lines \(l\) and \(m\) are parallel. Find \(x\).
Problem 8: Alternate interior angles
Lines \(l\) and \(m\) are parallel. Find \(x\).
Problem 9: Same-side interior angles
Lines \(l\) and \(m\) are parallel. Find \(x\).
Problem 10: Linear pair and vertical angles
Find \(x\) and \(y\).
Problem 11: Alternate exterior angles
Lines \(l\) and \(m\) are parallel. Find \(x\).
Problem 12: Corresponding angles with x
Two parallel lines are cut by a transversal. Corresponding angles measure \((3x+10)^{\circ}\) and \(70^{\circ}\). Find \(x\).
Problem 13: Same-side interior with x
Two parallel lines are cut by a transversal. Same-side interior angles measure \((2x+20)^{\circ}\) and \((x+40)^{\circ}\). Find \(x\) and both angles.
Problem 14: Triangle with x
The angles of a triangle measure \((x+10)^{\circ}\), \((2x)^{\circ}\) and \((3x+20)^{\circ}\). Find \(x\) and each angle.
Problem 15: Exterior angle with x
An exterior angle of a triangle measures \((5x-10)^{\circ}\). The remote interior angles measure \((2x+15)^{\circ}\) and \((x+25)^{\circ}\). Find \(x\) and the exterior angle.
Problem 16: All eight angles
Lines \(l\) and \(m\) are parallel and one angle measures \(74^{\circ}\). Find the measure of every labeled angle.
Problem 17: Same angles?
Triangle 1 has angles \(50^{\circ}\) and \(60^{\circ}\). Triangle 2 has angles \(60^{\circ}\) and \(70^{\circ}\). Are the triangles similar? Explain.
Problem 18: Not similar
Triangle 1 has angles \(45^{\circ}\) and \(65^{\circ}\). Triangle 2 has angles \(45^{\circ}\) and \(75^{\circ}\). Are the triangles similar? Explain.
Problem 19: Missing side by AA
Triangles \(ABC\) and \(DEF\) have two pairs of equal angles, marked below. Show that they are similar, then find \(EF\) when \(AB=6\), \(BC=8\) and \(DE=9\).
Problem 20: Roof truss
The top angle of an isosceles roof truss measures \(100^{\circ}\). Find the measure of each equal base angle \(x\).
Problem 21: City streets
Oak Street and Pine Street are parallel. Main Street crosses both. On the east side of Main, the angle between Main and Oak inside the strip between the two streets measures \(52^{\circ}\). Find the angle between Main and Pine inside the strip on the east side, and on the west side.
Problem 22: Parallel line through a vertex
Sofia draws a line through \(C\) parallel to side \(AB\) of triangle \(ABC\), where \(\angle A=58^{\circ}\) and \(\angle B=67^{\circ}\). The line makes angles \(x\) and \(z\) with the sides, as shown. Find \(x\), \(z\) and \(\angle C\), and show that \(x+\angle C+z=180^{\circ}\).
Problem 23: Ramp brace
Liam builds a triangular brace for a skateboard ramp. At one corner the exterior angle measures \(125^{\circ}\), and the interior angle at a different corner measures \(35^{\circ}\). That corner is not next to the exterior angle. Find all three interior angles of the brace.
Problem 24: Quilt seam
Mei sews a quilt with two parallel stripes cut by a diagonal seam. A pair of alternate interior angles measures \((4x+8)^{\circ}\) and \((6x-32)^{\circ}\). Find \(x\) and the measure of each angle.
See every chapter on the Grade 8 math page.