Sec 1 Mathematics Angles, Triangles & Polygons topical questions

Find each unknown angle, stating the angle fact you use.

1. (a)The supplement of a 47° angle.[1]
2. (b)Three angles at a point measuring 120°, 150° and x°.[1]
3. (c)Two angles on a straight line measuring 89° and y°.[1]

Classify each triangle by its angles: one with angles 30°, 60° and 90°; one with 100°, 40° and 40°; one with 80°, 60° and 40°.

Two parallel lines are cut by a transversal. One angle is 118°. Find the co-interior angle and the alternate angle.

A quadrilateral has three angles of 85°, 95° and 100°. Find the fourth angle.

Two parallel lines are cut by a transversal. One angle is (2x + 10)° and its corresponding angle is (3x − 20)°.

1. (a)Form an equation in x.[2]
2. (b)Solve for x.[1]
3. (c)State the size of the angles.[1]

Three angles of a quadrilateral measure 110°, 75° and 85°. Find the fourth angle.

In triangle ABC, angle A = 52° and angle B = 63°. The side BC is extended to D, forming exterior angle ACD.

1. (a)Find angle ACB.[2]
2. (b)Find angle ACD in two different ways, showing the working for each.[2]

In the figure, PQ is parallel to RS. A transversal crosses them so that one angle between the transversal and PQ is 3x°, the co-interior angle at RS is (x + 40)°.

1. (a)Form an equation in x.[2]
2. (b)Solve for x and state both angles.[2]

A regular polygon has 9 sides (a regular nonagon).

1. (a)Find the size of each exterior angle.[2]
2. (b)Find the size of each interior angle.[1]
3. (c)Find the sum of all the interior angles.[1]

A triangle has interior angles (2x − 5)°, (3x + 10)° and 65°.

1. (a)Form an equation in x.[1]
2. (b)Solve the equation to find x.[2]
3. (c)State all three angles.[1]

A park gazebo has a regular octagonal floor (8 equal sides).

1. (a)Calculate the exterior angle at each corner (the turn from one side to the next).[2]
2. (b)Find the interior angle at each corner.[1]
3. (c)Find the total of all the interior angles.[1]

In triangle PQR, the exterior angle at R measures 128°, and the triangle is isosceles with PQ = PR.

1. (a)Find angle PRQ.[1]
2. (b)Find the other two angles of the triangle.[3]
3. (c)State which two angles must be equal and why.[1]

A regular polygon has an interior angle of 165°.

1. (a)Find the size of each exterior angle.[1]
2. (b)Find the number of sides.[2]
3. (c)Name the polygon.[1]

In triangle ABC, angle B is a right angle. The bisector of angle A meets BC at D, and angle A = 56°.

1. (a)Find angle BAD and angle DAC.[1]
2. (b)Find angle ADB.[2]
3. (c)Find angle ADC, and explain the relationship between angles ADB and ADC.[2]

Triangle ABC is isosceles with AB = AC, and angle BAC = 80°. Angle ABC = (3x + 5)°.

1. (a)Find the size of each base angle.[1]
2. (b)Find x.[2]
3. (c)Find the exterior angle at C in two different ways.[2]