Angles, Parallel Lines and Triangles: Grade 8 Math Test – PDF Download

Question 1: Third angle (2 points)

Find the missing angle in each triangle.

1. A triangle has angles \(63^{\circ}\) and \(49^{\circ}\). (1 point)
2. A right triangle has an acute angle of \(28^{\circ}\). (1 point)

Question 2: Triangle with variables (2 points)

The angles of a triangle measure \((x+15)^{\circ}\), \((2x)^{\circ}\) and \((3x-15)^{\circ}\).

1. Find \(x\). (1 point)
2. Find the measure of each angle. (1 point)

Question 3: Exterior angles (2 points)

Use the triangle to answer part (a).

1. Find the exterior angle \(x\). (1 point)
2. A different triangle has an exterior angle of \(142^{\circ}\) and a remote interior angle of \(89^{\circ}\). Find the other remote interior angle. (1 point)

Question 4: Parallel lines and a transversal (3 points)

Lines \(l\) and \(m\) are parallel. Find each measure and name the angle relationship.

1. \(x\) (1 point)
2. \(y\) (1 point)
3. \(z\) (1 point)

Question 5: Alternate interior with x (2 points)

Two parallel lines are cut by a transversal. A pair of alternate interior angles measures \((4x-12)^{\circ}\) and \((2x+18)^{\circ}\).

1. Find \(x\). (1 point)
2. Find the measure of each angle. (1 point)

Question 6: Roof truss (2 points)

A roof truss is an isosceles triangle with a top angle of \(112^{\circ}\). The base is extended to form an exterior angle \(y\).

1. Find the base angle \(x\). (1 point)
2. Find \(y\). (1 point)

Question 7: Similar by angles (2 points)

Triangle \(ABC\) has angles \(35^{\circ}\) and \(80^{\circ}\). Triangle \(DEF\) has angles \(80^{\circ}\) and \(65^{\circ}\).

1. Find the third angle of each triangle. (1 point)
2. Are the triangles similar? Explain. (1 point)

Question 8: Missing side by AA (2 points)

In the figure, triangles \(ABC\) and \(DEF\) have equal marked angles. \(AB=8\), \(AC=10\) and \(DE=12\).

1. Find the scale factor from \(\triangle ABC\) to \(\triangle DEF\). (1 point)
2. Find \(DF\). (1 point)

Question 9: Why the angle sum is 180 (3 points)

A line through \(C\) is parallel to side \(AB\) of triangle \(ABC\), where \(\angle A=49^{\circ}\) and \(\angle B=63^{\circ}\).

1. Find \(x\) and \(z\) and name the angle relationship. (2 points)
2. Find \(\angle C\) and show that the angles along the line add to \(180^{\circ}\). (1 point)

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