A quadrilateral is made up of two triangles and sum of interior angles in a triangle add to 180°. So, sum of two triangles add to 360°, which means sum of interior angles in a quadrilateral is 360°.

Quadrilateral is a 4-sided two-dimensional closed figure. Rectangle, square, parallelogram, kite, rhombus, trapezoid are all different types of quadrilaterals.

#### Rectangle • Each angle in a rectangle is a right angle (90°).
• Opposite sides are of equal length and parallel to each other.

#### Square • Each angle in a square is a right angle (90°).
• All sides in a square are of equal length.
• Opposite sides are parallel to each other.

#### Parallelogram • Opposite sides in a parallelogram are parallel and equal in length.
• Opposite angles are also equal.

#### Trapezoid Pair of opposite sides in a trapezoid is parallel.

When the sides other than the parallel sides are equal to each other, then the trapezoid is called isosceles trapezoid. Also, the base angles in an isosceles trapezoid are equal to each other.

#### Rhombus All sides in a rhombus are of equal length.°

Opposite sides and angles are equal (like in a parallelogram).

Example: If 104°, 42°, and 65° are the three measures of a quadrialteral, then what is the measure of fourth angle?

The sum of angles in a quadrilateral is 360°.

Measure of given three angles = 104° + 42° + 65° = 211°

Measure of fourth angle = 360° – 211° = 149°

#### Check Point

1. What is the measure of angle C in the given parallelogram ABCD? 2. PQRS is an isosceles trapezoid. What is the measure of angle D? 3. Find the measure of angle R in given rhombus, PQRS. 4. What is the measure of angle C in given quadrilateral? 5. If an angle in a parallelogram measures 130°, then what is the measure of angle opposite to it?

1. 54°
2. 119°
3. 57°
4. 141°
5. 130°

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