Angle facts: Revision mini quiz

Work out the size of angle x

• 45

• 123

• 57

• 90

Answer explanation

Angle x is equal to 123 degrees because corresponding angles are equal.

Calculate the size of angle x

• 45

• 74

• 90

• 106

Answer explanation

Angle x and angle 74 degrees are co-interior and co-interior angles add to 180 degrees, therefore x = 180 - 74 = 106 degrees.

A triangle has angles 67° and 54°. What is the size of the third angle?

• 59°

• 90°

• 72°

• 45°

Answer explanation

To find the third angle, subtract the sum of the given angles (67° + 54°) from 180° (sum of angles in a triangle). Therefore, the third angle is 59°.

A quadrilateral has angles 83°, 149°, and 93°. What is the size of the fourth angle?

• 90

• 72

• 35

• 125

Answer explanation

The sum of angles in a quadrilateral is 360°. Therefore, the fourth angle is 360 - (83 + 149 + 93) = 35°.

A regular polygon has 15 sides. What is the size of each interior angle?

• 165 degrees

• 156 degrees

• 120 degrees

• 180 degrees

Answer explanation

The sum of interior angles in a polygon with n sides is given by (n-2) * 180 degrees. Therefore, each interior angle of a regular polygon with 15 sides is (15-2) * 180 / 15 = 156 degrees.

If an exterior angle of a regular polygon is 12°, how many sides does the polygon have?

• 24

• 36

• 40

• 30

Answer explanation

The sum of exterior angles of a polygon is always 360°. Since each exterior angle of the regular polygon is 12°, the polygon has 30 sides (360° / 12° = 30). Therefore, the correct answer is 30.

Work out the size of angle x

• 57

• 90

• 75

• 45

Answer explanation

Angle x is equal to 57 degrees because the angle 57 degrees is corresponding to the angle which is vertically opposite angle x. Vertically opposite angles are equal.

Work out the size of angle x

• 160

• 70

• 80

• 30

Answer explanation

Angle x, angle 80 degrees and angle corresponding to 30 degrees are adjacent on the same straight line. Corresponding angles are equal and angles on a straight line sum to 180 degrees therefore angle x = 180 - (80+30) = 70

Work out the size of angle x

• 48 degrees

• 38 degrees

• 94 degrees

• 90 degrees

Answer explanation

Angle x+38 degrees and angle 48 degrees are co-interior. Co-interior angles add to 180 degrees. Therefore angle x = 180 - (48+38) = 94 degrees.