Two angles are complementary when they add up to 90°. Think of them as "completing" a right angle corner. Two angles are supplementary when they add up to 180°. Think of them as "supplying" a straight line. If an angle measures 35°, what is the measure of its complement? What is the measure of its supplement?

When two lines cross, they create vertical angles (also called opposite angles). Vertical angles are the angles that are across from each other at the intersection point. The most important rule about vertical angles is that they are ALWAYS equal. Imagine an X shape – the top and bottom angles are vertical to each other, and the left and right angles are vertical to each other. If one angle at an intersection measures 72°, what is the measure of its vertical angle?

Adjacent angles share a common vertex and a common side, but do not overlap. They are "next to" each other. Think of two slices of pizza next to each other – they share the crust (common side) and meet at the tip (common vertex). For two angles to be adjacent, they must NOT overlap and they must NOT be vertical angles. Which description correctly defines adjacent angles?

When a line (called a transversal) crosses two parallel lines, it creates eight angles with special relationships. Corresponding angles are in the same position at each intersection – they are equal. Alternate interior angles are inside the parallel lines on opposite sides of the transversal – they are equal. Alternate exterior angles are outside the parallel lines on opposite sides – they are equal. Consecutive interior angles (inside, same side) are supplementary (add to 180°). If a transversal crosses two parallel lines and one angle measures 65°, what is the measure of its corresponding angle?

Any polygon (closed shape with straight sides) has an interior angle sum that follows a formula. For a triangle (3 sides), the sum is 180°. For a quadrilateral (4 sides), the sum is 360°. In general, for a polygon with n sides, the sum of interior angles = (n - 2) × 180°. A pentagon has 5 sides. What is the sum of its interior angles?

A regular polygon has all sides equal AND all angles equal. A square is a regular quadrilateral. An equilateral triangle is a regular triangle. A regular hexagon (like a honeycomb cell) has 6 equal sides and 6 equal angles. To find each interior angle of a regular polygon, divide the interior angle sum by the number of sides. A regular octagon has 8 sides. What is the measure of EACH interior angle?

A parallelogram is a quadrilateral with BOTH pairs of opposite sides parallel. Rectangles, squares, and rhombuses are special types of parallelograms. Important properties: opposite sides are equal, opposite angles are equal, consecutive angles are supplementary (add to 180°), and diagonals bisect each other (cut each other in half). In parallelogram ABCD, if angle A measures 110°, what is the measure of angle C (the opposite angle)?

A rectangle is a special parallelogram where all four angles are right angles (90°). Because it is a parallelogram, it inherits all parallelogram properties: opposite sides are parallel and equal, diagonals bisect each other. But rectangles have two additional properties: all angles are 90°, and the diagonals are CONGRUENT (equal in length). A rectangle has length 6 cm and width 8 cm. What is the length of each diagonal? (Hint: Use the Pythagorean Theorem!)

A circle is a set of all points at a fixed distance (the radius) from a center point. Important circle measurements: radius (r) = distance from center to any point on the circle. Diameter (d) = distance across the circle through the center = 2 × radius. Circumference (C) = distance around the circle = π × diameter = 2πr. Area (A) = space inside = πr². If a circle has a radius of 7 cm, what is its circumference? (Use π ≈ 3.14)

Every triangle has a special relationship between interior and exterior angles. An exterior angle is formed by extending one side of a triangle. The Exterior Angle Theorem states that an exterior angle equals the sum of the two remote interior angles (the two angles NOT adjacent to it). This theorem is extremely useful for finding unknown angles. In a triangle, one interior angle is 50° and another is 70°. What is the measure of the exterior angle adjacent to the third angle? (Hint: Find the third angle first, then its exterior angle supplement, OR use the Exterior Angle Theorem.)