Sec 3 E-Math Angles, Triangles & Polygons topical questions

Three angles lie on a straight line: 2x°, 3x° and 40°. Form an equation and find x.

Two straight lines cross and one of the four angles formed is 68°. Write down the sizes of the other three angles, with reasons.

Four angles at a point are x°, 2x°, 3x° and 120°. Find x and list all four angles.

Two parallel lines are cut by a transversal, and one of the eight angles is 124°. Find (a) its co-interior partner, (b) its corresponding angle, and (c) its alternate angle.

A right-angled triangle has angles 90° and 31°. Find the third angle.

The angles of a quadrilateral are 85°, 95°, 100° and x°. Find x.

The exterior angle at one vertex of a triangle is 118°, and the two remote interior angles are x° and (x + 26)°. Find x, state both remote angles, and find the third interior angle of the triangle.

The exterior angle at the apex of an isosceles triangle is 124°. Find all three interior angles of the triangle.

(a) Find the sum of the interior angles of a regular heptagon (7 sides). (b) Hence find the size of each interior angle, correct to 1 decimal place.

For a regular pentagon, find (a) each exterior angle and (b) each interior angle, and (c) verify your answers are consistent.

Each interior angle of a regular polygon is 156°. How many sides does the polygon have?

In trapezium ABCD, AB is parallel to DC, angle A = 70° and angle D = 65° (both on leg AD). Find angles B and C, which sit along leg BC.

Each interior angle of a regular polygon is 162°. (a) Find each exterior angle. (b) Find the number of sides. (c) Verify your answer using the interior-angle sum.

A pentagon has four equal angles of 110° and a fifth angle of y°. (a) Find the sum of the interior angles of a pentagon. (b) Find y. (c) Is the pentagon regular? Give a reason.

1. (a)Interior angle sum.[1]
2. (b)Find y.[2]
3. (c)Regular or not, with reason.[2]

Two co-interior angles between parallel lines measure (3x − 20)° and (2x + 10)°. (a) Form an equation in x. (b) Solve it. (c) State both angles and check their sum.

1. (a)Form the equation.[2]
2. (b)Solve for x.[1]
3. (c)State the angles and check.[2]

The angles of a triangle are x°, 2x° and 3x°. (a) Find x. (b) State all three angles and classify the triangle by its angles.

1. (a)Find x.[2]
2. (b)State and classify.[3]

In a right-angled triangle, one angle is 90° and the other two are x° and (x + 30)°. (a) Form an equation in x. (b) Find all three angles. (c) State the size of the exterior angle at each of the two acute vertices.

1. (a)Form the equation.[2]
2. (b)Find the angles.[2]
3. (c)Exterior angles at the acute vertices.[2]

(a) Describe fully, step by step, the construction of the perpendicular bisector of an 8 cm segment PQ using ruler and compasses. (b) Explain why every point on your constructed line is equidistant from P and Q. (c) A point R lies on the perpendicular bisector with PR = 5 cm; state QR with a reason.

1. (a)Describe the construction.[3]
2. (b)Explain the equidistance property.[2]
3. (c)State QR.[1]

In a regular polygon, each interior angle is 8 times each exterior angle. (a) Form an equation in the exterior angle e. (b) Find e. (c) How many sides does the polygon have?

1. (a)Form the equation.[2]
2. (b)Find e.[2]
3. (c)Number of sides.[2]

Triangle ABC is isosceles with AB = AC, and the exterior angle at B is 140°. (a) Find the interior angles at B and C. (b) Find the angle at A. (c) Find the exterior angle at A, and verify it equals the sum of the two remote interior angles.

1. (a)Angles at B and C.[2]
2. (b)Angle at A.[2]
3. (c)Exterior angle at A and verification.[2]