Angle Sum Property of a quadrilateral | Understanding Quadrilaterals | Assessment | English | Grade 8

Which of the following can be four interior angles of a quadrilateral?

• 90°, 140°, 90°, 140°

• 110°, 110°, 110°, 110°

• 50°, 70°, 90°, 150°

• 45°, 82°, 85°, 95°

Answer explanation

The sum of interior angles of a quadrilateral is 360°. Among the given options, the sum of measures of interior angles given in option 3 is 360°. 50° + 70° + 90° + 150° = 360° Hence, these angles must be interior angles of a quadrilateral. Therefore, option 3 is correct.

If the angles of a quadrilateral are (2x + 9°), (x - 2°), (3x + 8°) and (4x + 5°). What is the measure of largest interior angle of the quadrilateral?

• 150°

• 110°

• 77°

• 141°

Answer explanation

According to angle sum property, the sum of interior angles of a quadrilateral is 360°. So, (2x + 9°) + (x - 2°) + (3x + 8°) + (4x + 5°) = 360° i.e. 2x + x + 3x + 4x + 9° - 2° + 8° + 5° = 360° i.e. 10x + 20° = 360° i.e. 10x = 360° - 20° i.e. 10x = 340° i.e. x = 340°/10 i.e. x = 34° Hence, the angles of the quadrilateral must be, (2x + 9) = (2 x 34 + 9)° = 77° (x - 2)° = (34 - 2)° = 32° (3x + 8)° = (3 x 34 + 8)° = 110° (4x + 5)° = (4 x 34 + 5)° = 141° Largest angle is 141°

If the number of sides of a polygon is n, the sum of all interior angles of the polygon would be ___

• n x 180°

• n x 360°

• (n-2) x 180°

• (n-2) x 360°

Answer explanation

If the number of sides of a polygon is n, the sum of all interior angles of the polygon would be (n-2) x 180°

What is the value of x in the given figure?

• 90°

• 75°

• 120°

• 150°

Answer explanation

The sum of all angles of the quadrilateral = 360° Therefore, 75° + 90° + x + 120° = 360° i.e. x + 285° = 360° On transposing 285° to RHS of the equation, we get, x = 360° - 285° x = 75° Hence option 2 is the correct answer

In quadrilateral ABCD if ∠A = ∠C = 30° and ∠B = ∠D, what is the measure of ∠B?

• 60°

• 90°

• 150°

• 180°

Answer explanation

There are four angles in a quadrilateral. It is given that the opposite angles are equal. Let the unknown angle be x The sum of all interior angles of the quadrilateral = 360° Therefore, 30° + x 30° + x = 360° i.e. 2(30°+x) = 360° transposing 2 to RHS, we get, 30°+x = 360°/2 i.e. 30° + x = 180° transposing 30° to RHS, we get, x = 180° - 30° i.e. x = 150° Thus option 3 is the correct answer

In the given figure, BC || DE, and AC ||EF. What is the value of y?

• 54°

• 51°

• 75°

• 126°

Answer explanation

In the given figure, BC || DE, and AC ||EF. We know that the sum of interior angles of a triangle is 180° therefore, in △ABC ∠A + ∠B + ∠C = 180° therefore, 51° + 75° + ∠C = 180° i.e. 126° + ∠C = 180° i.e. ∠C = 180° - 126° = 54° Since BC || DE, therefore ∠C = ∠CDE = 54°.... (Alternate interior angles) Since EF || DG therefore ∠CDE = ∠DEF = 54° i.e. y = 54°

Rahul took seven matchsticks of equal length. He made a polygon by using all of them. What is the sum of the interior angles of the polygon so formed?

• 360°

• 720°

• 900°

• 1000°

Answer explanation

Since the length of seven matchsticks are equal therefore the polygon formed will be a regular heptagon. The sum of interior angles of a regular polygon = (n-2) x 180° where n is the number of sides of the polygon. So, for heptagon i.e. a polygon with number of sides, n = 7, Sum of interior angles of heptagon = (7-2) x 180° = 5 x 180° = 900° hence option 3 is correct