**Introduction to angle 180 degrees:**

The angle 180 degrees are present in the triangle, straight angle and in the supplementary angle. If the sum of the two angles up to 180 called as the supplementary angle. The sum of the three angles in triangle will be 180 degrees and the straight line consists of the angle180 degrees. In geometry, only few will be exactly 180 degrees. Now we are going to see about the angle 180 degrees.

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The two adjacent angles in a straight line are given in the ratio as 5: 10. Determine the two angles.

**Solution:**

Let us assume the first angle be 6x and other angle be 8x

5x + 10x = 180

15x =180

Divide by 15 on both sides we get,

x = `180/15`

x = 12

5x = 5 × 12 = 60

10x = 10 × 12 = 120

The adjacent angles are = 75 and 120 degrees.

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**Example 1:**

The two angles of an acute triangle are given as 50° and 60°. Determine the third angle of the triangle?

**Solution:**

The sum of the three angles of a triangle = 180°

The sum of the given two angles = 60° + 30° = 90°

Hence, the third angle of triangle = 180° – 90° = 90°

Thus, the third angle is 90 degree.

**Example 2:**

Determine the supplementary angle of 68°.

**Solution:**

The supplementary angle of 68° = 180° – 68° = 112°.

The supplementary angle of 112° = 180° – 112° = 68°.

The angles 68° and 112° are supplementary angles.

**Example 3:**

Determine the angle in the right angle triangle where one of the angles is given as 46 degrees?

**Solution:**

In the right triangle, one of the angle will be 90 degrees and another angle is 46

The sum of three angles in triangle = 180

90 + 46 + x = 180

136 + x = 180

x = 180 - 136

x = 44 degrees

Thus the third angle is 44 degrees.

**Example 4:**

Determine the supplementary angle of 78°.

**Solution:**

The supplementary angle of 78° = 180° – 78° = 122°.

The supplementary angle of 122° = 180° – 122° = 78°.

The angles 78° and 122° are supplementary angles.