# EQUATION PRACTICE WITH ANGLE ADDITION

To solve problems in this topic, we have to analyze the following.

Check the relationship between the angles involving.

## Complementary and Supplementary

(i) If they are complementary to each other, they will add upto 90.

(ii) If they are supplementary, they will add upto 180.

(i) In triangle, sum of interior angle is 180.

(ii) In triangle, the exterior angle is equal to sum of remote interior angles.

## Parallel Lines and Transversal

When two lines are parallel and they cut by the transversal, the following pairs will be congruent.

• Corresponding angles
• Alternate interior angles
• Alternate exterior angles
• Vertically opposite angles will be equal.

Sum of consecutive interior angles on the same side of the transversal will be equal to 180 degree.

Example 1 :

Find the value of x. Solution :

By observing AOB, it is complementary. So, sum of the angles is 90.

x + 20 = 90

Subtracting 20 on both sides, we get

x = 90 - 20

x = 70

Example 2 :

Find x. Solution :

∠AOC = ∠BOD (Vertically opposite angles)

2x + 25 = 50

Subtracting 25 on both sides, we get

2x = 50 - 25

2x = 25

Dividing by 2 on both sides.

x = 25/2

x = 12.5

Example 3 :

Find x. Solution :

AOB is a straight line. Its angle measure is 180.

∠AOC + ∠BOC = 180

60 + 5x + 5 = 180

5x + 65 = 180

Subtracting 65.

5x = 180 - 65

5x = 115

Divide by 5.

x = 115/5

x = 23

Example 4 :

Find x. Solution :

∠XYZ = ∠XYW + ∠WYZ

50 = 2x + 30

Subtracting 30.

2x = 50 - 30

2x = 20

Dividing by 2.

x = 20/2

x = 10

Example 5 :

Find x. Solution :

By observing the picture given above, they are vertically opposite angles.

-2x - 6 = 40

-2x = 40 + 6

-2x = 46

Dividing by -2 on both sides.

x = 46/(-2)

x = -23

Example 6 :

Find the value of x. Solution :

∠XYW = 3x + 2

∠WYZ = 72

∠XYZ = 110

∠XYW + ∠WYZ = ∠XYZ

3x + 2 + 72 = 110

3x + 74 = 110

Subtracting 74 on both sides.

3x = 110 - 74

3x = 36

Dividing by 3 on both sides.

x = 36/3

x = 12

Example 7 :

Find the angle B. Solution :

In triangle ABC,

∠A + ∠B + ∠C = 180

Here C = 90, ∠A = 46

46 + ∠B + 90 = 180

136 + ∠B = 180

∠B = 180 - 136

∠B = 44

Example 8 :

Find ∠JKX Solution :

Using exterior angle theorem.

∠JKX = ∠KLJ + ∠LJK

∠JKX = 93 + 44

∠JKX = 137

Example 9 :

Find the value of x. Solution :

In the triangle, the sum of interior angles is 180.

2x + 1 + 5x + 5 + 90 = 180

By combining the like terms, we get

7x + 96 = 180

Subtracting 96 on both sides.

7x = 180 - 96

7x = 84

Dividing by 7 on both sides.

x = 84/7

x = 12

Example 10 :

Find the value of x and y. Solution :

From the picture, the opposite sides are parallel.

So, 3x and 5x-20 are alternate angles.

3x = 5x - 20

-2x = -20

x = 10

Sum of interior angle of triangle = 180

2y + 4y + 5x - 20 = 180

6y + 5x - 20 = 180

6y + 5x = 180 + 20

6y + 5x = 200 -------(1)

Applying the value of x  in (1)

6y + 5(10) = 200

6y + 50 = 200

By subtracting 50 on both sides.

6y = 200 - 50

6y = 150

Dividing by 6 on both sides, we get

y = 150/6

y = 25

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