This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Quadrilaterals – Sum Angle Property”.

1. What is the general formula to count the sum of all the interior angles of a polygon with ‘n’ number of sides?

a) 180°

b) 360°

c) 90°

d) 720°

View Answer

Explanation: The general formula for the sum total of all the interior angles of any polygon is (n-2)180°. For example: As we know that the sum of all the interior angles of any triangle is 180°.

So, now we can recheck it with the above formula.

*Sum of interior angles*=(n-2)180°

Any triangles have three sides so n=3.

∴

*Sum of interior angles*=(3-2)180°

∴

*Sum of interior angle*=180°.

2. What is the sum of all the angles in any triangle?

a) 90°

b) 180°

c) 270°

d) 240°

View Answer

Explanation: : As we know that the sum of all the interior angles of any triangle is 180°.

*Sum of interior angles*=(n-2)180°

Any triangles have three sides so n=3.

∴

*Sum of interior angles*=(3-2)180°

∴

*Sum of interior angle*=180°.

3. If the angles of a four sided polygon are in the ratio 7:8:9:12, then the angles would be?

a) 70, 80, 90, 100

b) 70, 70, 80, 80

c) 120, 70, 80, 100

d) 70, 80, 90, 120

View Answer

Explanation: Let us assume x to be the common multiple.

Now, the sides of the four sided polygon would be 7x, 8x, 9x and 12x.

The sum total of any four sided polygon is 360°.

Therefore 7x+8x+9x+12x=360

Therefore 36x=360

Therefore x=10°

Therefore the angles are, 7x=70, 8x=80, 9x=90 and 12x=120.

One can recheck their answer by, verifying the total as One can recheck their answer by, verifying the total as 360°.

4. In a triangle the sides are 4 cm, 5 cm and 4 cm. One of the base angle is 80°. Find the measure of the apex angel.

a) 30°

b) 40°

c) 20°

d) 10°

View Answer

Explanation: One can get the hint that the given triangle is isosceles triangle by observing the length of all the sides. As in an isosceles triangle two sides are of equal length and also the base angles are equal in measure. Let the apex angle for denoted by the variable x.

Therefore 80+80+x=180

Therefore 160+x=180

Therefore x=20.

5. A four sided polygon has all sides equal in length, what would be the angle between two adjacent sides?

a) *Exactly* 90°

b) 90° *or any acute angle*

c) 90° *or any obtuse angle*

d) *Can be any angle*

View Answer

Explanation: When a four sided polygon has its all sides equal in length it is a square. Any square has it’s angles =90°. Hence the answer would be 90°. Here the other options won’t be accurate. For example if a student selects the option 90° or

*any acute angle*it would be partially correct because in a square the angles are always right angles.

6. In a quadrilateral the angles are 40°,120°,10° and x. Find x.

a) 40°

b) 120°

c) 190°

d) 180°

View Answer

Explanation: A quadrilateral is a four sided polygon. Therefore the sum of all the interior angles is 360°.

Therefore 40+120+10+x=360

Therefore 170+x=360

Therefore x=190.

7. What angle is subtended by a semicircle?

a) 360°

b) 300°

c) 180°

d) 90°

View Answer

Explanation: A circle subtends a whole of 360°, this is the measure of one complete rotation over the circumference of the circle. Now, the semicircle would subtend an angle of 180°.

8. What would be the measure of all the angles in a scalene triangle?

a) 60°, 60° and 60°

b) 120°, 30° and 30°

c) 90°, 45° and 45°

d) 60°, 30° and 90°

View Answer

Explanation: In a scalene triangle the measure of all the angles and the sides is different. The options other then 60°, 30° and 90° are either equilateral triangles or isosceles triangles.

9. Any right angled triangle must have how may angles in total?

a) Two angles

b) Four angles

c) One angle

d) Three angles

View Answer

Explanation: In any triangle irrespective of any type of triangle it has three angles in total. Here if the question would ask the ‘how many angles other than right angle’ then the answer would be two angles.

10. The formula (n-2)180° is the formula for the sum of exterior angle of ‘n’ sided polygons.

a) True

b) False

View Answer

Explanation: The formula (n-2)180° is the formula for the interior angles of the polygon.

As we know the sum angle property of the square is 360°.

Therefore (n-2)180°

Therefore (4-2)180°

Therefore 360°.

**Sanfoundry Global Education & Learning Series – Mathematics – Class 8**.

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