Angle Sum Property of a Triangle

Q.

Question 108

In the given figure, find the value of x.

Q.

Can a triangle have two right angles?

Q.

Question 121

Each of the two equal angles of an isosceles triangle is four times the third angle. Find the angles of the triangle.

Q.

Question 5

In an isosceles triangle, one angle is ${70}^{\circ }$. The other two angles are of

i) ${55}^{\circ }$ and ${55}^{\circ }$
ii) ${70}^{\circ }$ and ${40}^{\circ }$
iii) Any measure

In the given option(s) which of the above statement(s) are true?

a) (i) only
b) (ii) only
c) (iii) only
d) (i) and (ii)

Q.

If one angle of a triangle is less than $90$ degrees, it is known as an acute-angled triangle.

1. False

2. True

Q.

Question 125

Find the values of x and y in the given figure.

Q.

Find the value of the unknown x in the following diagrams:

Q.

Question 40

In $\Delta ABC$, $\angle A={100}^{\circ }$, AD bisects $\angle A$ and $AD\perp BC$. Then, $\angle B$ is equal to

a) ${80}^{\circ }$
b) ${20}^{\circ }$
c) ${40}^{\circ }$
d) ${30}^{\circ }$

Q.

Question 107

The measure of three angles of a triangle are in the ratio 5 : 3 : 1. Find the measures of these angles.

Q.

Question 131

In $\Delta PQR$, if $3\angle P=4\angle Q=6\angle R$, calculate the angles of the triangle.

Q. The sum of all three interior angles in an acute-angled triangle is equal to .

1. 45${}^{\circ }$
2. 90${}^{\circ }$
3. 180${}^{\circ }$

Q.

Question 2 (ii)
Find the values of unknowns x and y in the following diagram:

Q.

Question 30

Which of the following triplets cannot be the angles of a triangle?
a) ${67}^{\circ },{51}^{\circ },{62}^{\circ }$
b) ${70}^{\circ },{83}^{\circ },{27}^{\circ }$
c) ${90}^{\circ },{70}^{\circ },{20}^{\circ }$
d) ${40}^{\circ },{132}^{\circ },{18}^{\circ }$

Q. If ∆ ABC ≅ ∆ PQR, then AB and AC will be equal to ______ and _______ respectively.

1. PQ, QR
2. QR, PR
3. PQ, PR
4. QP, RQ

Q.

Question 129

In the given figure, find the values of x, y and z.

Q.

The sum of the two angles in a triangle is 95${}^{\circ }$ and their difference is 25${}^{\circ }$. Then which of the following are true?

1. 75°, 50°, 55°

2. 85°, 65°, 30°

3. 50°, 45°, 85°

4. 60°, 35°, 85°

Q.

Question 127

The angles of a triangle are arranged in descending order of their magnitudes. If the difference between two consecutive angles is ${10}^{\circ }$, find the three angles.

Q.

Question 110

In $\Delta XYZ$, the measure of $\angle X$ is ${30}^{\circ }$ greater than the measure of $\angle Y$ and $\angle Z$ is a right angle. Find measure of $\angle Y$

Q.

Question 1 (iv)
Find the value of unknown x in the following isosceles triangle:

Q.

Question 1 (iii)
Find the value of unknown x in the following diagrams.

Q.

Question 27

If one of the angle of a triangle is ${110}^{\circ }$, then the angle between the bisectors of the other two angles is

a) ${70}^{\circ }$
b) ${110}^{\circ }$
c) ${35}^{\circ }$
d) ${145}^{\circ }$

Q.

Question 1 (v)
Find the value of unknown x in the following diagrams.

Q.

Question 2 (iii)
Find the values of unknowns x and y in the following diagram:

Q.

If the measures of two of the angles of a triangle are 25 degrees and 60 degrees, then the third angle is _____.

1. 85°

2. 105°

3. 75°

4. 95°

Q.

Question 111

In a $\Delta ABC$, the measure of an $\angle A$ is ${40}^{\circ }$ less than the measure of $\angle B$ and $\angle C$ is ${50}^{\circ }$ more than that of $\angle A$. Find the measure of $\angle A$.

Q.

Question 14

If in an isosceles triangle, each of the base angle is ${40}^{\circ }$, then the triangle is

a) Right angled triangle
b) Acute angled triangle
c) Obtuse-angled triangle
d) Isosceles right-angled triangle

Q.

Which of the following triangles are isosceles as well as obtuse-angled triangles?

1. Fig 1 and Fig 3 only

2. Fig 2 and Fig 3 only

3. Fig 1, Fig 2 and Fig 3 only

4. Fig 1, Fig 2 and Fig 4 only

Q.

Question 2

$\Delta DEF$ in the given figure is a right-angled triangle with $\angle E={90}^{\circ }$. What type of angles are $\angle D$ and $\angle F$?

a) They are equal angles
b) They form a pair of adjacent angles
c) They are complementary angles
d) They are supplementary angles

Q.

Question 109

In the given figures (i) and (ii), find the values of a, b and c.

Q. Angles of a triangle are $(x+{10}^{\circ })(x+{40}^{\circ })$ and $(2x-{30}^{\circ }$. What is the value of x?

1. ${30}^{\circ }$
2. ${40}^{\circ }$
3. ${20}^{\circ }$
4. ${10}^{\circ }$