Angle Sum Property

Q. Every triangle has atleast acute angles.

1. One
2. Two
3. Three

Q.

A triangle with all the three angles less than 60 degree is possible. (True/False)

1. True

2. False

Q.

Is the sum of any two angles of a triangle always greater than the third angle?

Q.

We can draw exactly one triangle whose angles are $70°,30°\mathrm{and}80°$. Say True or False

1. True
2. False

Q. Find the value of x in the following triangle.

1. ${60}^{\circ }$
2. ${40}^{\circ }$
3. ${120}^{\circ }$
4. ${80}^{\circ }$

Q.

Which of the following cannot be the measure of three angles of a triangle?

1. ∠A = 60°, ∠B = 60°, ∠C = 60°

2. ∠A = 70°, ∠B = 20°, ∠C = 100°

3. ∠A = 90°, ∠B = 90°, ∠C = 90°

4. ∠A = 72°, ∠B = 30°, ∠C = 78°

Q.

Question 47

Name the following angles of the given figure using three letters.

a) $\angle 1$
b) $\angle 2$
c) $\angle 3$
d) $\angle 1$ + $\angle 2$
e) $\angle 2$ + $\angle 3$
f) $\angle 1$ + $\angle 2$+$\angle 3$
g) $\angle CBA$ - $\angle 1$

Q.

If one angle of a right angled triangle measures ${25}^{\circ },$ then find the measure of the other acute angle.

1. ${50}^{\circ }$

2. ${70}^{\circ }$

3. ${65}^{\circ }$

4. ${55}^{\circ }$

Q. Find the complementary angle of ${20}^{\circ }+y^{\circ }$

Q.

In a triangle ABC , angle A is half of B and angle C is thrice of A . Find the value of angle A, B and C? [4 MARKS]

Q.

Question 51

Will the measures of $\angle ABC$ and $\angle CBD$ make the measure of $\angle ABD$ in the figure?

Q.

If the angles of a triangle are in the ratio 1 : 2 : 3, then the smallest angle is ___.

1. 60°

2. 30°

3. 15°

4. 45°

Q.

In the figure, $\angle BAD=4\angle DBA$, what is the measure of $\angle ABC$ and x in degrees?

1. ${15}^{\circ },{45}^{\circ }$
2. ${60}^{\circ },{45}^{\circ }$
3. ${30}^{\circ },{60}^{\circ }$
4. ${60}^{\circ },{30}^{\circ }$

Q.

The three angles of a triangle are in the ratio of $3:8:4$. Find the measure of each angle.

Q.

The angles of a triangle are in the ratio 3:5:7. What are the angles?

1. 36${}^{\circ }$, 60${}^{\circ }$, 84${}^{\circ }$

2. 32${}^{\circ }$, 66${}^{\circ }$, 82${}^{\circ }$

3. 34${}^{\circ }$, 60${}^{\circ }$, 86${}^{\circ }$

4. 46${}^{\circ }$, 50${}^{\circ }$, 84${}^{\circ }$

Q. In triangle ABC, which side will lie opposite to $\angle A$ ? [1 MARK]

Q. In $△ABC$, $AB=AC$ and $\angle B={40}^{\circ }$. What is the value of $\angle C$(in degree)?

1. 40

Q.

In the given figure, if $\angle ABD={120}^{\circ }$ and $\angle ACE={135}^{\circ },$ then $x^{\circ }$ = ___.

1. ${60}^{\circ }$

2. ${80}^{\circ }$

3. ${70}^{\circ }$

4. ${75}^{\circ }$

Q.

Consider the figure:

If $BC=AC,x=2y,$ and angle $\angle ACB={60}^{\circ },$ then the value of $\angle B+y$ is ___ (in degrees).

Q.

A triangle can have all the three angles greater than ${60}^{\circ }$.

1. True

2. False

Q. In triangle ABC, which side will lie opposite to $\angle A$? [1 MARK]

Q. If sum of two angles of a triangle is ${60}^o$. Then, the measure of third angle of a triangle is:

1. ${60}^o$
2. ${90}^o$
3. ${120}^o$
4. ${180}^o$

Q.

Bisectors of interior $\angle B$ and exterior $\angle ACD$ of a$\Delta ABC$ intersect at the point $T$. Prove that $\angle BTC=\frac{1}{2}\angle BAC$

Q.

The measures of three angles of a triangle are in the ratio $1:2:3$. Then the triangle is

Q. Find the value of $\angle C$ in the below triangle if the value of $\angle CAB$ = 25${}^o$. If AB = BD, then what can be the value of $\angle D$ [3 MARKS]

Q. Find the value of x in the below diagram.
[3 MARKS]

Q. In the figure given below, LOM is a straight line. What is the value of x?

Q. In a right angled $△ABC$, right-angled at B, $\angle A+\angle C$ =

1. ${90}^{\circ }$
2. ${120}^{\circ }$
3. ${180}^{\circ }$
4. ${45}^{\circ }$

Q.

In the figure given below, If AB || CD and CD || EF and y : z = 3 : 7, find x.

1. None of these
2. 
3. 
4. 

Q.

State whether the statements are true or false.

A triangle can have three acute angles.

1. True
2. False