Step: 1

[Sum of the interior angles of a triangle is 180°.]

Step: 2

55° + 65° + ∠ ACB = 180°

[Substitute.]

Step: 3

120° + ∠ ACB = 180°

[Add.]

Step: 4

[Subtract 120 on both the sides.]

Step: 5

[Angle made by a straight line is 180°.]

Step: 6

[Substitute.]

Step: 7

[Subtract 60 on both the sides.]

Step: 8

So, the value of x is 120°.

Correct Answer is : 120°

Step: 1

[Linear pair.]

Step: 2

Step: 3

The sum of the measures of the angles of a triangle is 180.

[Triangle angle sum theorem.]

Step: 4

[From step 3.]

Step: 5

[Simplify.]

Step: 6

So, z + y = 120 + 30 = 150

Correct Answer is : 150

Step: 1

In ΔA B C , m ∠ A B C = 54 and m ∠ B A C = 86

Step: 2

Since side B C is extended to the point D , exterior angle of ∠ A C B is ∠ A C D .

Step: 3

The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.

[Exterior angle theorem.]

Step: 4

[From step 3.]

Step: 5

54 + 86 = m ∠ A C D

[Substitute the values of ∠ ABC and ∠ BAC.]

Step: 6

[Simplify.]

Step: 7

So, the measure of the marked exterior angle of the triangle is 140.

Correct Answer is : 140

Step: 1

From the figure, ∠ B A C = 90° and ∠ A B D = 108°.

Step: 2

The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.

[Exterior angle theorem.]

Step: 3

[From step 2.]

Step: 4

90° + (x - 54)° = 108°

[Substitute.]

Step: 5

36° + x = 108°

Step: 6

[Subtract 36 from both sides.]

Step: 7

So, the value of x in the figure is 72°.

Correct Answer is : 72°

Step: 1

From the figure, ∠ CAB = 63° and ∠ ABD = 136°.

Step: 2

The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.

[Exterior Angle Theorem.]

Step: 3

[From step 2.]

Step: 4

63° + y ° = 136°

[Substitute.]

Step: 5

[Subtract.]

Step: 6

So, the measure of y is 73°.

Correct Answer is : 73°

Step: 1

If one side of a triangle is produced, then the exterior angle so formed is equal to the sum of the interior opposite angles.

Step: 2

Step: 3

Step: 4

50° = 30° + x °

Step: 5

Step: 6

Step: 7

Therefore, the measure of x is 20°

Correct Answer is : 20°

Step: 1

In ΔABC, ∠ ABC = 52° and ∠ BAC = 89°

Step: 2

Since side BC is extended to the point D, exterior angle of ∠ ACB is ∠ ACD.

Step: 3

The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.

[Exterior angle theorem.]

Step: 4

[From step 3.]

Step: 5

52° + 89° = ∠ ACD

[Substitute the values of ∠ ABC and ∠ BAC.]

Step: 6

[Simplify.]

Step: 7

So, the measure of the marked exterior angle of the triangle is 141°.

Correct Answer is : 141°

- Parallel Lines and Transversals-Gr 8-Solved Examples
- Angle Sum Theorem of a Triangle-Gr 8-Solved Examples
- Pythagorean Theorem-Gr 8-Solved Examples
- Distance Between Two Points-Gr 8-Solved Examples
- Transformations-Gr 8-Solved Examples
- Volume of Cylinders-Gr 8-Solved Examples
- Volume of Cones-Gr 8-Solved Examples
- Volume of a Sphere-Gr 8-Solved Examples

- Exterior Angle