Step: 1

The sum of three angles in a triangle is 180°.

Step: 2

Step: 3

[Substitute ∠
B = 60° and ∠
C = 61°.]

Step: 4

[Combine like terms.]

Step: 5

[Subtract 121° from both sides.]

Step: 6

Correct Answer is : 59°

Step: 1

From the figure, AC = BC.

Step: 2

So, ΔABC is isosceles and ∠ A = ∠ B.

Step: 3

Let ∠ A = ∠ B = x

Step: 4

In a triangle, the sum of all the angles is equal to 180°.

Step: 5

Step: 6

[Substitute ∠ A = ∠ B = x and ∠ C = 34°.]

Step: 7

2x = 180° - 34°

[Subtract 34° from each side.]

Step: 8

2x = 146°

Step: 9

[Divide each side by 2.]

Step: 10

Correct Answer is : 73°

Step: 1

In an isosceles triangle, two angles are equal.

Step: 2

A triangle with angle measures 30°, 30°, 120° and 30°, 75°, 75° forms an isosceles triangle.

Step: 3

Among the choices, a triangle with angle measures 30°, 40°, and 120° cannot form an isosceles triangle.

Correct Answer is : 40°, 120°

Step: 1

Sum of the four angle measures in a quadrilateral is 360^{o}.

Step: 2

Let x be the measure of the fourth angle.

Step: 3

Step: 4

Step: 5

[Subtract 277 from both sides.]

Step: 6

Step: 7

So, the measure of the fourth angle is 83^{o}.

Correct Answer is : 83^{o}

Step: 1

The adjacent angles in a parallelogram are supplementary.

Step: 2

In parallelogram ABCD, ∠ A and ∠ B are adjacent angles.

Step: 3

m∠ A + m∠ B = 180°

Step: 4

50° + m∠ B = 180°

[Substitute m∠ A = 50°.]

Step: 5

[Subtract 50° on both sides.]

Step: 6

m∠ B = 130°

Step: 7

In a parallelogram, opposite angles are congruent.

Step: 8

Step: 9

m∠ C = m∠ A = 50°

Step: 10

Step: 11

m∠ D = m∠ B = 130°

Step: 12

m∠ B = 130°, m∠ C = 50° and m∠ D = 130°

Correct Answer is : 130°, 50°, 130°

Step: 1

The sum of three angles in a triangle is 180°.

Step: 2

Let x be the third angle.

Step: 3

Step: 4

[Substitute sum of two angles = 120°.]

Step: 5

[Subtract 120° from each side.]

Step: 6

Step: 7

The third angle is 60°.

Correct Answer is : 60°

Step: 1

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

Step: 2

The measure of the third angle = 180 - (50 + 40).

Step: 3

= 90

[Simplify]

Step: 4

So, the measure of the third angle is 90.

Correct Answer is : 90

Step: 1

The given diagram is a quadrilateral with four angles.

Step: 2

In a quadrilateral, the sum of the four angles = 360°

Step: 3

So, ∠50 + ∠120 + ∠ 80 + ∠x = 360°

Step: 4

∠250 + ∠x = 360°

Step: 5

Therefore, ∠x = 360° - 250° = 110°

Correct Answer is : 110°

Step: 1

The given diagram is a quadrilateral with four angles.

Step: 2

In a quadrilateral, the sum of the four angles = 360°.

Step: 3

So, 79° + 100° + 106° + y° = 360°.

Step: 4

y° + 285° = 360°

Step: 5

Therefore, y° = 360° - 285° = 75°.

[Simplify.]

Correct Answer is : 75°

Step: 1

In a quadrilateral, the sum of the four angles = 360°.

Step: 2

[PQRS is a quadrilateral.]

Step: 3

87° + 78° +90° + m ∠ S = 360°

[Substitute the given values.]

Step: 4

255° + m ∠ S = 360°

[Simplify.]

Step: 5

[Subtract.]

Step: 6

So, m ∠ S is 105°.

Correct Answer is : 105°

Step: 1

Let the unknown angle be x .

Step: 2

90° + 90° + 52° + x ° = 360°

[The given figure is a quadrilateral.]

Step: 3

232° + x ° = 360°

[Simplify.]

Step: 4

[Subtract.]

Step: 5

So, the measure of the unknown angle is 128°.

Correct Answer is : 128°

Step: 1

Sum of the four angle measures in a quadrilateral is 360°.

Step: 2

Let x be the measure of the fourth angle.

Step: 3

Step: 4

Step: 5

[Subtract 240 from both sides.]

Step: 6

Step: 7

So, the measure of the fourth angle is 120°.

Correct Answer is : 120°

Step: 1

Sum of the four angle measures in a quadrilateral is 360°.

Step: 2

Let x be the measure of the fourth angle.

Step: 3

Step: 4

[Subtract 250 from both sides.]

Step: 5

Step: 6

So, the measure of the fourth angle is 110°.

Correct Answer is : 110°

Step: 1

The sum of all the angle measures of a triangle is 180°.

Step: 2

90° + 62° + y ° = 180°

[Equate the sum of angles of the triangle to 180°.]

Step: 3

152° + y ° = 180°

[Add.]

Step: 4

[Subtract 152° from each side.]

Correct Answer is : 28°

Step: 1

The sum of all the angle measures of a triangle is 180°.

Step: 2

In the triangle, the sum of all the 3 angles measures is 30° + 40° + X .

Step: 3

30° + 40° + X = 180°

[Equate the sum of all the three angles measures of the triangle to 180°.]

Step: 4

70° + X = 180°

Step: 5

[Subtract 70° on both sides.]

Step: 6

So, the measure of the third angle of the triangle is 110°.

Correct Answer is : 110°

- Complementary, Supplementary, Vertical and adjacent Angles-Gr 7-Solved Examples
- Scale Drawings-Gr 7-Solved Examples
- Application Problems involving Scale Drawings-Gr 7-Solved Examples
- Solving Problems on Area of a Circles-Gr 7-Solved Examples
- Circumference of Circles-Gr 7-Solved Examples
- Perimeter and Area of Composite Figures-Gr 7-Solved Examples

- Triangle
- Triangle Proportionality Theorem