Angles and Shapes

What is the sum of angles in a triangle?

• A180°✓
• B90°
• C270°
• D360°

Answer: The angles in any triangle always add up to 180°.

In a triangle, two angles are 50° and 60°. What is the third angle?

• A30°
• B60°
• C70°✓
• D120°

Answer: Third angle = 180° - 50° - 60° = 70°.

What is the sum of angles in a quadrilateral?

• A360°✓
• B270°
• C540°
• D180°

Answer: The angles in any quadrilateral add up to 360°.

What is the sum of angles in a pentagon?

• A480°
• B720°
• C540°✓
• D360°

Answer: Sum of angles = (5 - 2) × 180° = 3 × 180° = 540°.

What is the size of each interior angle in a regular hexagon?

• A150°
• B90°
• C120°✓
• D135°

Answer: Sum of angles in hexagon = (6 - 2) × 180° = 720°. Each angle = 720° ÷ 6 = 120°.

What is the size of each interior angle in a regular octagon?

• A120°
• B144°
• C135°✓
• D150°

Answer: Sum = (8 - 2) × 180° = 1080°. Each angle = 1080° ÷ 8 = 135°.

Two angles are vertically opposite. If one is 65°, what is the other?

• A115°
• B65°✓
• C130°
• D25°

Answer: Vertically opposite angles are equal. So the other angle is also 65°.

Two angles on a straight line are supplementary. If one is 35°, what is the other?

• A65°
• B145°✓
• C55°
• D155°

Answer: Angles on a straight line add up to 180°. So the other angle = 180° - 35° = 145°.

In a parallelogram, if one angle is 75°, what is the opposite angle?

• A165°
• B75°✓
• C105°
• D15°

Answer: Opposite angles in a parallelogram are equal. So the opposite angle is also 75°.

In a parallelogram, if one angle is 60°, what are the adjacent angles?

• A60° and 120°✓
• B60° and 60°
• C120° and 120°
• D60° and 90°

Answer: Adjacent angles in a parallelogram are supplementary (add to 180°). So 180° - 60° = 120°.

When two parallel lines are cut by a transversal, what can we say about alternate angles?

• AThey are equal✓
• BThey are supplementary
• CThey add to 90°
• DThey add to 270°

Answer: Alternate angles formed by parallel lines and a transversal are equal.

Two parallel lines are cut by a transversal. If one alternate angle is 55°, what is the other?

• A145°
• B35°
• C55°✓
• D125°

Answer: Alternate angles are equal, so the other angle is also 55°.

What is the name of a quadrilateral with four equal sides?

• ATrapezium
• BRectangle
• CKite
• DRhombus✓

Answer: A rhombus is the quadrilateral defined by having four equal sides. A kite has two pairs of equal adjacent sides, a rectangle has two pairs of equal sides, and a trapezium has one pair of parallel sides.

What is the sum of an exterior angle and its adjacent interior angle?

• A360°
• B180°✓
• C90°
• D270°

Answer: An exterior angle and its adjacent interior angle are supplementary (on a straight line), so they add to 180°.

What type of angle is 95°?

• ARight
• BReflex
• CAcute
• DObtuse✓

Answer: An obtuse angle is between 90° and 180°. 95° is obtuse.

If a bearing from A to B is 050°, what is the bearing from B to A?

• A310°
• B230°✓
• C130°
• D050°

Answer: The return bearing is 180° different. 050° + 180° = 230°.

A triangle has angles in the ratio 2:3:4. What are the angles?

• A35°, 53°, 92°
• B50°, 60°, 70°
• C40°, 60°, 80°✓
• D30°, 45°, 105°

Answer: Ratio 2:3:4 means 9 parts total. Each part = 180° ÷ 9 = 20°. Angles are 2×20°=40°, 3×20°=60°, 4×20°=80°.

What is the sum of the interior angles of a hexagon?

• A720°✓
• B360°
• C540°
• D900°

Answer: Sum of interior angles = (n - 2) × 180° where n is the number of sides. For n = 6: (6 - 2) × 180 = 720°.

What is each interior angle of a regular pentagon?

• A90°
• B144°
• C120°
• D108°✓

Answer: Sum of interior angles = (5 - 2) × 180 = 540°. Each angle = 540 ÷ 5 = 108°.

What is each exterior angle of a regular hexagon?

• A90°
• B45°
• C60°✓
• D30°

Answer: The sum of exterior angles of any polygon is 360°. For a regular hexagon with 6 sides: 360 ÷ 6 = 60°.

What is the sum of the interior angles of a quadrilateral?

• A180°
• B540°
• C720°
• D360°✓

Answer: Sum = (4 - 2) × 180 = 360°.

Three of the interior angles of a quadrilateral are 85°, 100° and 62°. What is the size of the fourth angle?

• A103°
• B247°
• C113°✓
• D293°

Answer: The interior angles of a quadrilateral add up to 360°. The three known angles total 85 + 100 + 62 = 247°, so the fourth angle is 360 - 247 = 113°. Using 540° (the pentagon total) would give 293°.

What is the size of each interior angle of a regular octagon?

• A45°
• B135°✓
• C120°
• D1080°

Answer: The exterior angle of a regular octagon is 360 / 8 = 45°, so each interior angle is 180 - 45 = 135°. The 1080° figure is the total of all eight interior angles, and 120° belongs to a regular hexagon.

What is the relationship between opposite angles in a cyclic quadrilateral?

• AThey are equal
• BOne is twice the other
• CThey sum to 90°
• DThey sum to 180°✓

Answer: In a cyclic quadrilateral, opposite angles sum to 180°.

Two parallel lines are cut by a transversal. If one angle is 120°, what is the alternate angle?

• A180°
• B60°
• C120°✓
• D240°

Answer: Alternate angles are equal when parallel lines are cut by a transversal. So the alternate angle is also 120°.

Two parallel lines are cut by a transversal. If one angle is 75°, what is the corresponding angle?

• A255°
• B105°
• C180°
• D75°✓

Answer: Corresponding angles are equal when parallel lines are cut by a transversal. So the corresponding angle is 75°.

Two parallel lines are cut by a transversal. If one angle is 65°, what is the co-interior angle?

• A180°
• B125°
• C65°
• D115°✓

Answer: Co-interior angles (same-side interior) sum to 180°. So 180 - 65 = 115°.

Prove that the sum of the angles in a triangle is 180°. Which statement is correct?

• AIt's obvious from drawing
• BMeasure all angles with a protractor
• CUse the exterior angle theorem
• DDraw a line parallel to one side through the opposite vertex. Use alternate angles.✓

Answer: A proof involves drawing a line parallel to the base through the opposite vertex and using alternate angles to show the three angles sum to 180°.

The exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. If two interior angles are 50° and 70°, what is the exterior angle?

• A180°
• B130°
• C60°
• D120°✓

Answer: By the exterior angle theorem, the exterior angle equals the sum of the two non-adjacent interior angles: 50° + 70° = 120°.

A regular polygon has an exterior angle of 24°. How many sides does it have?

• A12
• B24
• C10
• D15✓

Answer: The exterior angles of any polygon add up to 360°. For a regular polygon, the number of sides = 360 ÷ exterior angle = 360 ÷ 24 = 15.

A regular octagon has 8 sides. What is each interior angle?

• A45°
• B135°✓
• C180°
• D90°

Answer: Sum = (8 - 2) × 180 = 1080°. Each angle = 1080 ÷ 8 = 135°.