# Finding Angle Measures

Home | Online Math Tutoring | 8th Grade Math Tutoring | **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 Ð*AOB*. The measure of Ð*AOB* 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°.

**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.

*∠ 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°)

(2*x* – 3) + (2*x* + 4) + (*x* + 9) = 90°

5*x* + 10 = 90

5*x* = 80 => *x *= 16

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

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

*∠DOB* = *x* + 9 = 16 + 9 = **25****°**

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

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

3*x* + 21 = 90

3*x* = 69 implies *x *= 23

**CHECK POINT **

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

##### Answer key

- 118°
- 29
- 110°
- 34°
- 45°

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