how to find an angle of a right triangle

How to Detect the Mensurate of an Bending in a Triangle: iii Methods

how to find the measure of an angle: Chalk drawn triangle with a triangle ruler and chalks over a blue board

If you want to know how to find the measure of an angle within a triangle, the nigh obvious mode is to use a protractor. But if you don't accept one on hand, hither are 3 ways to discover the measure of an angle within a triangle.

How to Notice the Mensurate of an Angle

The sum of the angles of a triangle always add up to 180 degrees. So when you subtract the given angles of a triangle from 180, you'll find the unknown angles. See the triangle below. The known angles are 77 and 35. To observe the unknown angle, nosotros must add these up and subtract them from 180:

how to find the measure of an angle: Illustration of a triangle with an unknown angle

77 + 35 = 112

180 - 112 = 68

Using Exterior Angles to Find Unknown Measurements

Supplementary angles are two angles that add up to 180 degrees. When yous put these two angles together, they make a straight angle:

how to find the measure of an angle: Illustration of a triangle with a straight angle

The rule of supplementary angles can be used to notice unknown angle measurements. See the obtuse triangle below where a measure of an angle outside of the triangle is 148 degrees. Since the line that this outside angle lies on is straight, the mensurate of the angle 148 and the unknown bending must add upwards to 180:

Obtuse triangle with an unknown interior angle

Let's subtract this exterior bending from 180 to make up one's mind the unknown interior angle:

180 - 148 = 32

Finding the Unknown Angle of a Right Triangle

If you are dealing with a correct triangle, finding the missing angle simply requires you to follow the rules of complementary angles. Since ane of the angles in a right triangle is 90 (and the angles of a triangle must add up to 180 degrees) the other two angles of the triangle must be acute angles (less than 90 degrees each) that add to 90 degrees.

Right triangle with an unknown third angle

In the above triangle ABC, angle a is a right bending, bending b is 30 degrees, and bending c is unknown. You can find the third bending c by subtracting 30 from 90:

90 - 30 = 60

Deciding How to Find the Mensurate of an Angle

Determining the measure of an angle inside a triangle is simple when you take the right methods. Once you know how to find an unknown angle using supplementary angles, complementary angles, and correct angles, you'll have mastered the art of unknown angles. Now you'll know how to make up one's mind unknown angles on your trigonometry tests without a calculator or protractor!