7.8 Angles

Two equal angles sit on a straight line. Find the size of each angle. Justify that they sum to 180°.

Two angles on a straight line are 112° and an unknown angle. Calculate the unknown angle. Show the subtraction and verify the pair sums to 180°.

Four angles meet at a point. Three of them are 100°, 75°, and 60°. Calculate the fourth angle and verify all four sum to 360°.

A triangle has angles 90° and 35°. Calculate the third angle and verify all three sum to 180°.

A quadrilateral has angles 110°, 70°, and 95°. Calculate the fourth angle and verify all four sum to 360°.

Two lines cross and form four angles. One angle is 117°. Calculate all four angles and check they sum to 360°.

An angle on a straight line measures 74°. Calculate its supplementary angle (the other angle on the straight line) and show they add to 180°.

An isosceles triangle has two equal base angles. The angle at the top is 70°. Calculate each base angle, showing the subtraction and division. Check your answer.

A pair of parallel lines is cut by a transversal. One co-interior angle is 73°. Calculate the other co-interior angle and verify both sum to 180°.

A pair of parallel lines is cut by a transversal. One alternate angle is 131°. State and justify the alternate angle on the other side. Then calculate the co-interior angle on the same side.

Find angle $x$. Two angles on a straight line are $x$ and 48°.

Three angles meet at a point on a straight line: 43°, 98°, and $x$. Find $x$.

A triangle has angles $x$, 72°, and 39°. Find $x$.

An isosceles triangle has a top angle of 70°. Find each base angle.

A quadrilateral has three angles: 95°, 88°, 102°. Find the fourth angle $x$.

Find the exterior angle of a regular 9-sided polygon.

Find the interior angle of a regular 8-sided polygon.

Two parallel lines are cut by a transversal. A corresponding angle is 64°. Find the angle marked $x$ on the same side of the transversal, between the parallel lines (co-interior).

Two lines cross. One angle is 113°. Find all four angles formed.

An equilateral triangle has all sides equal. What is each interior angle?

A triangle has angles $x$, $2x$, and 24°. Find $x$ and the largest angle.

Two angles on a straight line are $(3x + 10)°$ and $(5x − 18)°$. Find $x$ and each angle.

Two angles on a straight line are in the ratio 1 : 5. Find each angle.

A quadrilateral has angles $x$, $x + 20°$, $2x$, and $x − 10°$. Find $x$ and each angle.

Two parallel lines are cut by a transversal. One alternate angle is $(4x − 12)°$ and the other is $(2x + 18)°$. Find $x$.

A regular polygon has 10 sides. Find its interior angle and state the name of the polygon.

A regular polygon has an exterior angle of 15°. How many sides does it have?

A protractor reading shows an angle of 97.4°. A second angle is 49.4° smaller. Find the second angle and state its type.

The exterior angle of a triangle is 134°. One of the non-adjacent interior angles is 67°. Find the other non-adjacent interior angle.

An angle is $\frac{5}{12}$ of a full turn. Find the angle in degrees and state its type.

Two parallel lines are cut by a transversal. A co-interior angle is $(5x + 8)°$ and the other co-interior angle is $(3x + 4)°$. Find $x$ and both angles.

A pie chart shows three sectors. The first sector represents 25% of the data and the second represents 45%. Find the angle of the third sector.

A regular polygon has interior angles of 140°. How many sides does it have? Then find its exterior angle.

In a triangle, angle A is twice angle B, and angle C is 15° more than angle A. Find all three angles.

A triangle has angles in the ratio $1 : 3 : 5$. Find each angle.

A survey asks 200 people their favourite colour. 90 choose blue, 50 choose red, and the rest choose green. Find the pie chart angle for green.

Use the formula (n − 2) × 180° to find the sum of interior angles of a 11-sided polygon. Then find each interior angle if it is regular.

A triangle has angles 47.6°, 81.5°, and $x$°. Find $x$, giving your answer as a decimal.

A kite has two pairs of equal angles. The angles are $x$, $x$, 130°, and 50°. Find $x$.

A bearing is measured clockwise from North. A ship sails on a bearing of 310°. How many degrees short of a full turn is this? Give the reflex angle formed on the other side of North.