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This mock test of Test: Angles Sum Property A Triangle for Class 9 helps you for every Class 9 entrance exam.
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QUESTION: 1

An exterior angle of triangle is 80° and the interior opposite angles are in the ratio 1:3. Measure of each interior opposite angle is:

Solution:
We know that,ext. angle=into.opp angle1+into.opp angle2let the common factor in the ratio be x.then Angle are x and 3xx +3×=804× =80×=203×=60 the answer is option D.

QUESTION: 2

In fig. if x°, y° and z° are exterior angles of ΔABC, then x° + y° + z° is:

Solution:

QUESTION: 3

The angles of a triangle are in the ratio 2 : 3 : 4. The angles, in order, are :

Solution:

QUESTION: 4

The angles of a triangle are in the ratio 2:3:4.So, the degree measures of the angles are

Solution:

QUESTION: 5

The value of x in the given figure is

Solution:

QUESTION: 6

In ΔABC fig., ∠x + ∠y + ∠z is equal to:

Solution:
Sum of exterior angles of a triangle is always 360

QUESTION: 7

The measure of angle a in the figure below is :

Solution:

QUESTION: 8

In fig., in ΔABC, AB = AC. The value of x is:

Solution:
AB=AC so angle. c = angle b in tri. abc .. now using angle sum property we'll get that angle B and C = 50degree each .. now, angle C + x =180 degree. [ linear pair] 50deg. + x =180 deg. x= 130 deg. Ans.

QUESTION: 9

The sum of two angles of a triangle is 116° and their difference is 24°. The measure of each angle of the triangle is

Solution:

Let us consider the sum of two angles as ∠A+∠B=116∘ and the difference can be written as ∠A−∠B=24^{o}

We know that the sum of all the angles in a triangle is 180^{o}.

So we can write it as

∠A+∠B+∠C=180^{o}

By substituting ∠A+∠B=116^{o} in the above equation

116^{o }+ ∠C = 180^{o}

On further calculation

∠C=180^{o }− 116^{o}

By subtraction

∠C=64^{o}

It is given that ∠A−∠B=24^{o}

It can be written as ∠A=24^{o}+∠B

Now by substituting ∠A=24^{o}+∠Bin∠A+∠B=116^{o}

∠A+∠B=116^{o}

24^{o}+∠B+∠B=116^{o}

On further calculation

24^{o}+2∠B=116^{o}

By subtraction

2∠B=116^{o}−24^{o}

2∠B=92^{o}

By division

∠B=292

∠B=46∘

By substituting ∠B=46∘ in ∠A=24∘+∠B

We get

∠A=24^{o}+46^{o}

By addition

∠A=70^{o}

Therefore, ∠A=70^{o},∠B=46^{o} and ∠C=64^{o}

QUESTION: 10

The three angles of a triangle, one is twice the smallest and another one is thrice the smallest.find the angles

Solution:

QUESTION: 11

The bisectors of the base angles of an isosceles triangle ABC, with AB = AC, meet at O. If ∠B = ∠C = 50Â°. What is the measure of angle O?

Solution:
The answer is b ,because in triangle OBC, angle OBC =25 degree, OCB =25degee and angle O is not given so, sum of all the angles will be 50 + angle O = 180 degreeangle O = 180-50angle O =130 degree

QUESTION: 12

In a triangle ABC if ∠A = 53° and ∠C = 44° then the value of ∠B is:

Solution:
B=180-(A+C) B=180-53+44 B=180-97 B=83

QUESTION: 13

Find the measure of angle marked e in the figure below:

Solution:
D+e=180(angles on linear pair),but d=30(vertically opposite angles),30+e=180,e=180-30,e=150

QUESTION: 14

If in triangle DEF, the greatest angle is twice the smallest and the third angle is 20 degrees more than the smallest, what are the angles?

Solution:

QUESTION: 15

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

Solution:
An exterior angle of a triangle is formed, when a side of a triangle is produced. The measure of any exterior angle of a triangle is equal to the sum of the measures of its two interior opposite angles. The sum of the three angles of a triangle is 180degree.

### Examples: Angle Sum Property of Triangle

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### Examples: Angle Sum Property of a Triangle

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### Proof: Angle Sum Property of Triangle

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