Solved Examples on Adjacent Angle
Example 1: Find the measures of two complementary adjacent angles if one angle measures 45°.
Solution:
If two angles are complementary, their measures add up to 90°. In this case, we know one angle measures 45°. To find the other angle, we subtract 45 from 90:
90° – 45° = 45°
So, the other angle also measures 45°. Therefore, the two complementary adjacent angles are both 45°.
Example 2: In a right triangle, one of the acute angles measures 30°. Find the measure of the other acute angle.
Solution:
In a right triangle, one of the acute angles is always 90°. The other two angles are the acute angles. If one acute angle measures 30°, we can find the measure of the other acute angle by subtracting 30 from 90:
90° – 30° = 60°
The other acute angle measures 60°.
Example 3: In a right triangle, one of the acute angles measures 40°. Find the measure of the other acute angle.
Solution:
In a right triangle, one of the acute angles is always 90°, and the sum of the measures of the acute angles is 90°. So, to find the measure of the other acute angle when one angle is 40°, subtract 40° from 90°:
Other acute angle = 90° – 40° = 50°
The measure of the other acute angle is 50°.
Example 4: If two vertical angles are formed by intersecting lines, and one of them measures 75°, what is the measure of the other vertical angle?
Solution:
Vertical angles are always congruent, which implies they measure the same. Given that one vertical angle measures 75°, the other vertical angle will also measure 75°.
Example 5: Two adjacent angles are complementary. If one angle measures 35°, find the measure of the other angle.
Solution:
If two angles are complementary, their measures add up to 90°. Given that one angle measures 35°, we can find the other angle by subtracting 35° from 90°:
Other angle = 90° – 35° = 55°
So, the other angle measures 55°, and the two adjacent angles are 35° and 55°.
What is Adjacent Angle in Geometry?
Adjacent Angles are the angles that have a common vertex, a common arm, and the rest two arms lie on either side of the common arm. Angles are particularly important in geometry as they help define and understand different geometric figures and their characteristics. Geometry is a branch of mathematics that focuses on shapes, sizes, and angles. A key concept within geometry is adjacent angles. Understanding adjacent angles helps us grasp the geometry of lines, polygons, and other shapes.
In this particular article, we are going to learn about adjacent angles, their definitions, their properties, and some examples and we will also practice some questions on it.
Table of Content
- What is an Adjacent angle?
- Properties of Adjacent Angle
- Adjacent Angles in Parallelogram
- Supplementary Adjacent Angles
- Complementary and Adjacent Angles
- Non-adjacent angles
Contact Us