Angles on a straight line sum to…?
\( 180^\circ \).
Angles & Polygons
8 exam-style questions on angles in parallel lines, triangles and regular polygons.
3 Easy 3 Medium 2 Hard
In a triangle, two angles are \( 50^\circ \) and \( 70^\circ \). Find the third angle.
\( 180 - 50 - 70 = 60^\circ \).
Corresponding angles are equal. Alternate angles are equal. Co-interior angles sum to…?
\( 180^\circ \).
Find the exterior angle of a regular hexagon.
\( \dfrac{360^\circ}{6} = 60^\circ \).
Find the interior angle of a regular octagon.
Exterior \( = 45^\circ \). Interior \( = 180 - 45 = 135^\circ \). Or \( \dfrac{(8-2)\times 180}{8} = 135^\circ \).
The sum of the interior angles of a polygon is \( 1260^\circ \). How many sides does it have?
\( (n-2) \times 180 = 1260 \) ⇒ \( n-2 = 7 \) ⇒ \( n = 9 \).
In a parallelogram ABCD, angle A is \( 70^\circ \). Find the other three angles.
Opposite angles equal: \( \angle C = 70^\circ \). Adjacent angles sum to \( 180^\circ \): \( \angle B = \angle D = 110^\circ \).
A regular polygon has interior angle \( 150^\circ \). How many sides does it have?
Exterior \( = 30^\circ \). Number of sides \( = \dfrac{360}{30} = 12 \).