# How to Find Missing Angels in Quadrilateral Shapes

## Step by step guide to Find Quadrilateral angles

The following diagram shows a quadrilateral $$ABCD$$ and the sum of its internal angles. A perfect quadrilateral is a surface obtained from the intersection of four lines and their extension. The sum of the internal angles of each triangle is $$180$$ degrees, and since each quadrilateral is made up of two triangles, the sum of the internal angles of each quadrilateral is $$360$$ degrees. Thus, $${\angle}A+{\angle}B+{\angle}C+{\angle}D=360^{\circ}$$.

A rectangle is a type of quadrilateral in which both adjacent sides are perpendicular to each other and form right angles. all a rectangle’s angles are $$90^{\circ}$$. $${\angle}A+{\angle}B+{\angle}C+{\angle}D=360^{\circ}$$.

A square is a quadrilateral, in other words, it is a geometric shape that has four sides, all of which are equal to each other and form a $$90-$$degree or right angle with each other. $${\angle}A+{\angle}B+{\angle}C+{\angle}D=360^{\circ}$$.

The parallelogram is a simple quadrilateral with two pairs of parallel sides. The size of the opposite sides and the opposite angles in the parallelogram are equal. $${\angle}A+{\angle}B+{\angle}C+{\angle}D=360^{\circ}$$.

### Finding Quadrilateral angles Example 1:

Find the missing angle in the quadrilateral.

Solution: We have been given three angles and need to determine the measure of the fourth. Add together the measures of the known angles.

$$125^{\circ}+90^{\circ}+105^{\circ}=320^{\circ}$$

Subtract the sum from $$360^{\circ}$$ to determine what remains for the fourth angle. $$360^{\circ}-320^{\circ}=40^{\circ}$$

The measure of the unknown angle is $$40^{\circ}$$

### Finding Quadrilateral angles Example 2:

Find the missing angle in the quadrilateral.

Solution: We have been given three angles and need to determine the measure of the fourth. Add together the measures of the known angles.

$$78^{\circ}+85^{\circ}+57^{\circ}=220^{\circ}$$

Subtract the sum from $$360^{\circ}$$ to determine what remains for the fourth angle. $$360^{\circ}-220^{\circ}=140^{\circ}$$

The measure of the unknown angle is $$140^{\circ}$$

## Exercises for Finding Quadrilateral angles

### Find the missing angle in each quadrilateral.

1)$$x=$$

2)$$x=$$

3)$$x=$$

1. $$x=75^{\circ}$$
2. $$x=70^{\circ}$$
3. $$x=62^{\circ}$$

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