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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.

finding angle measures

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°.

finding angle measures

Right Angle

One fourth the rotation will have a measure of 90°, which is called a ‘right angle’.

Acute Angle

An angle with a measure less than 90° is called an ‘acute’ angle.

Obtuse Angle

An angle with its measure lying between 90° and 180° is called an ‘obtuse’ angle.

Reflex Angle

An angle with its measure lying between 180° and 360° is called a ‘reflex’ angle.

Adjacent Angles

Two angles which have a common vertex and have a common arm are called ‘adjacent’ angles.

finding angle measures
finding angle measures

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

finding angle measures
finding angle measures

 

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

findingangle6-300x271

∠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.                                                                                                                                                         findingangle8-300x152
  2. If (5a + 42)° and (22 – a)° are supplementary angles, find a.
  3. Find the measure of DOC.                                                                           findingangle9-300x292
  4. AB and CD intersect at O. If AOD = 146°, find BOD.                          findingangle10-300x167
  5. Find x in the given figure.                                                                                                                                                                                                                                                            findingangle11-300x182
Answer key
  1. 118°
  2. 29
  3. 110°
  4. 34°
  5. 45°

 

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