8th Grade Angles in Triangles and Parallel Lines Worksheet (PDF)

8th Grade math worksheet: Angles in Triangles and Parallel Lines – Maths PDF

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This grade 8 angle relationships worksheet for 8th Grade covers angles in triangles and parallel lines (Common Core 8.G.A.5), with a free PDF to print.

These 21 problems practice angle relationships in triangles and with parallel lines cut by a transversal (Common Core 8.G.A.5). Each problem has its own space for work, so print the page and write directly on it.

The problems start with direct skill checks and grow harder as you go. Later items use algebra to find angles and use angles to decide whether triangles are similar. Use the answer key afterwards to check every step.

Grade 8 · Common Core State Standards: 8.G.A.5

Grade 8 angle relationships worksheet: exercises 1 to 10

Exercise 1 – Third angle

Find the third angle. Not drawn to scale.

A triangle has angles of \(52^{\circ}\) and \(79^{\circ}\). Find the third angle.

Exercise 2 – Angle ratio

The angles of a triangle measure \(2x\), \(3x\) and \(4x\) degrees. Find each angle.

Exercise 3 – Exterior angle

Exterior angle at B. Not drawn to scale.

A triangle has remote interior angles \(55^{\circ}\) and \(40^{\circ}\). Find the exterior angle \(x\).

Exercise 4 – Missing remote angle

An exterior angle of a triangle is \(130^{\circ}\) and one remote interior angle is \(50^{\circ}\). Find the other remote interior angle.

Exercise 5 – Vertical angles

Two lines cross. One angle is \((3x + 10)^{\circ}\) and its vertical angle is \((5x – 20)^{\circ}\). Find \(x\) and the angle.

Exercise 6 – Linear pair

Two angles form a linear pair. One measures \(112^{\circ}\). Find the other.

Exercise 7 – Corresponding angles

Lines j and k are parallel.

Lines \(j\) and \(k\) are parallel. Find \(x\) and name the angle pair.

Exercise 8 – Alternate interior

Lines j and k are parallel.

Lines j and k are parallel. Find the measure of the angle marked ?.

Exercise 9 – Solve with corresponding angles

Lines j and k are parallel.

Lines \(j\) and \(k\) are parallel. Find \(x\).

Exercise 10 – Co-interior angles

Two parallel lines are crossed by a transversal. Two same-side interior angles measure \((4x + 10)^{\circ}\) and \((2x + 20)^{\circ}\). Find \(x\) and each angle.

Exercises 11 and up

Exercise 11 – All eight angles

Lines j and k are parallel.

One angle formed by a transversal on parallel lines measures \(65^{\circ}\). Find the measures of the other seven angles.

Exercise 12 – AA similarity

Triangle 1 has angles \(40^{\circ}\) and \(70^{\circ}\). Triangle 2 has angles \(70^{\circ}\) and \(70^{\circ}\). Are the triangles similar?

Exercise 13 – Another similarity check

Triangle \(P\) has angles \(50^{\circ}\) and \(60^{\circ}\). Triangle \(Q\) has angles \(60^{\circ}\) and \(80^{\circ}\). Are they similar?

Exercise 14 – Prove the exterior angle

Show that an exterior angle of a triangle equals the sum of the two remote interior angles. Use angles \(a\), \(b\) and \(c\).

Exercise 15 – Roof truss

A roof truss with equal base angles. Not drawn to scale.

A roof truss is an isosceles triangle with apex angle \(100^{\circ}\) and two equal base angles \(x\). Find \(x\).

Exercise 16 – Street map

Main Street and Oak Street are parallel; Elm Avenue crosses both.

Main Street and Oak Street are parallel and Elm Avenue crosses both. At one crossing an angle measures \(72^{\circ}\). Find the co-interior angle on the same side at the other crossing.

Exercise 17 – Sign angles

A triangular sign has angles \(x^{\circ}\), \((x + 10)^{\circ}\) and \((x + 20)^{\circ}\). Find the angles.

Exercise 18 – Garden exterior angle

A triangular garden has an exterior angle of \(112^{\circ}\) at one corner. One remote interior angle is \(47^{\circ}\). Find the other remote interior angle and the interior angle at that corner.

Exercise 19 – Check the triangle

Can a triangle have angles \(85^{\circ}\), \(60^{\circ}\) and \(40^{\circ}\)? Explain.

Exercise 20 – Angle puzzle

In triangle \(ABC\), angle \(B\) is twice angle \(A\), and angle \(C\) is \(30^{\circ}\) more than angle \(A\). Find all three angles.

Exercise 21 – Explain the angle sum

Explain, using a line parallel to the base, why the angles of a triangle add to \(180^{\circ}\).

Key facts behind this grade 8 angle relationships worksheet

Key facts

Angles of a triangle: \(a + b + c = 180^{\circ}\).
Exterior angle = sum of the two remote interior angles.
Parallel lines: corresponding and alternate interior angles are equal.
Co-interior angles add to \(180^{\circ}\); vertical angles are equal.
Two equal angles are enough to show two triangles are similar (AA).

How to use this grade 8 angle relationships worksheet

Work through the exercises in order: they go from simple to challenging. Write every step on paper, then compare with the solutions page and redo any exercise you missed the next day.

Download the grade 8 angle relationships worksheet as a PDF with the button below and keep it with your notes.

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