Finding Angle Measures

The straight lines OA and OB meet at the point ‘O’, which is called the vertex of the angle AOB. OA and OB are the arms of the angle AOB. The amount of turning from OA to OB is called the measure of ÐAOB. The measure of ÐAOB does not depend upon the length of arms OA, OB of the angle.

If the straight line segment OA rotates about ‘O’ through a complete rotation then it will come back to its own position. This complete rotation is divided into 360 equal parts. Each part is called a degree and it is denoted by ‘°’. The measure of half the rotation is 180°.

∠ AOB and ∠ BOC  are adjacent angles with OB as the common arm.

Example: If ∠AOB = 90°, find the value of ∠AOE, ∠EOD and ∠DOB.

∠AOE + ∠EOD + ∠DOB = 90° (Given ∠AOB = 90°)

(2x – 3) + (2x + 4) + (x + 9) = 90°

5x + 10 = 90

5x = 80 => x = 16

So, ∠AOE = 2x – 3 = (2 × 16) – 3 = 32 – 3 = 29°

∠EOD = 2x + 4 = (2 × 16) + 4 = 32 + 4 = 36°

∠DOB = x + 9 = 16 + 9 = 25°

Example: If (2x + 17)° and (x + 4)° are complementary, what is the value of x?

(2x + 17) + (x + 4) = 90° (Given as complementary angles)

3x + 21 = 90

3x = 69 implies x = 23

Check Point

1. Find the value of ∠YOZ, if XOY is a straight line.                                                                                                                                                        
2. If (5a + 42)° and (22 – a)° are supplementary angles, find a.
3. Find the measure of ∠DOC.                                                                          
4. AB and CD intersect at O. If ∠AOD = 146°, find ∠BOD.                         
5. Find x in the given figure.                                                                                                                                                                                                                                                           

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