Angle Sum Property for Triangles

Q.

In a rhombus ABCD the altitude from D to side AB, bisects AB . Find the angles of the rhombus.

Q.

In a isoceles traingle each base angle is 30' greater than the vertical angle . Find the measure of all the three angles of the triangles.

Q.

Triangle are in ratio 4 ratio 5 is sum of two angle equal third angle find angles

Q.

Of the three angles of a triangle the second one is one third of the first and the third angle is 26 degree more than the first angle find all the three angles of the triangle

Q.

Find the value of x in the given triangle.

1. ${20}^{\circ }$
2. ${30}^{\circ }$
3. ${25}^{\circ }$
4. ${35}^{\circ }$

Q.

Statement 1: A triangle in which each angle is acute is called an acute angle triangle.

Statement 2: A triangle in which each angle is obtuse is called an obtuse angle triangle.

1. Both statements are true.
2. Both statements are false.
3. Statement 1 is false and statement 2 is true.
4. Statement 1 is true and statement 2 is false.

Q. In a triangle ABC, $AB=AC$ and $\angle$B = 30${}^{\circ }$. Then value of $\angle A$ is .

1. ${20}^{\circ }$
2. ${30}^{\circ }$
3. ${40}^{\circ }$
4. ${50}^{\circ }$

Q. In $△ABC$, if $\angle B=\angle C={45}^{\circ }$, then which of the following is/are the longest side(s)?

1. AB
2. AC
3. AB and BC
4. BC

Q. In the given figure $\angle ABP=\angle ACQ,\angle BAC={68}^{\circ }$. Find the measure of $\angle ABC$.

1. ${124}^{\circ }$
2. ${56}^{\circ }$
3. ${60}^{\circ }$
4. ${52}^{\circ }$

Q. How to prove that " In a quadrilateral, the sum of all exterior eangles is 360 degrees.?

Q.

What is the measure of the largest angle of a triangle whose angles are in the ratio 4 : 5 : 9?

1. 50^o

2. 100^o

3. 40^o

4. 90^o

Q.

How many triangles can be drawn having its angles as $53°,64°$ and $63°$? Give reason for your answer.

Q.

In a convex hexagon, prove that the sum of all interior angle is equal to the sum of its exterior angles formed by producing the sides in the same order.

Q.

In the given figure, the value of 'x' and 'y' is:

1. $X={45}^{\circ },Y={75}^{\circ }$
2. $X={30}^{\circ },Y={55}^{\circ }$
3. $X={45}^{\circ },Y={30}^{\circ }$
4. $X={60}^{\circ },Y={75}^{\circ }$

Q. Question 8
Show that the angles of an equilateral triangle are ${60}^{\circ }$ each

Q.

The vertical angle of an isosceles triangle is $30°$ more than each of its base angles. find all the angles of the triangle.

Q.

In a convex hexagon prove that the sum of all interior angle is equal to the twice the sum of its exterior angle formed by producing the sides in the same order

Q.

In $\Delta RST$, $RS$ = 5 cm, $\angle SRT={45}^{\circ }$ and $\angle RST={45}^{\circ }$. Which criterion can be used to construct $\Delta RST$?

1. A.A.S. criterion

2. A.S.A. criterion

3. S.A.S. criterion

4. S.S.S. criterion

Q.

(a) Can a triangle have two obtuse angles? Justify your answer.
(b) In a $△ABC$ the side BC is extended to D. Given that $\angle ABC={30}^{\circ }and\angle ACD={160}^{\circ }$. Find $\angle BAC$. [3 MARKS]

Q.

The measure of two angles of a triangle are $105°$ and $20°55‵$. Find the measure of the third angle.

Q.

Find the value of unknown $x$ in the following diagram.

Q.

The minute hand when it moves $330°$ from $11$ oclock, is now at ?

1. $9\mathrm{O}\mathrm{clock}$

2. $11\mathrm{O}\mathrm{clock}$

3. $12\mathrm{O}\mathrm{clock}$

4. $10\mathrm{O}\mathrm{clock}$

Q.

Find the measure of $\angle BAE$ in the following figure.

1. ${15}^{\circ }$
2. ${75}^{\circ }$
3. ${45}^{\circ }$
4. ${30}^{\circ }$

Q. One angle of a triangle is ${82}^{\circ }$ and the other two are in the ratio 3 : 4. Find the value of other two angles.

1. ${38}^{\circ }$ and ${60}^{\circ }$
2. ${54}^{\circ }$ and ${44}^{\circ }$
3. ${42}^{\circ }$ and ${56}^{\circ }$
4. ${48}^{\circ }$ and ${50}^{\circ }$
   

Q.

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

Q.

In a triangle ABC, angle A =110° and AB=AC , find angle B and angle C

Q. The sum of all interior angles of quadrilateral is

1. 90 degrees
2. 180 degrees
3. 360 degrees
4. 270 degrees

Q.

With reference to the figure below, consider the two statements:

Statement I: The points A, B, and C will lie on a straight line if x + y = ${180}^{\circ }$.

Statement II: If the angle between two lines is ${180}^{\circ }$, then all the points on both the lines lie on a straight line.

1. Both the statements are true but statement 2 is not the correct explanation of statement 1

2. Both the statements are true and statement 2 is the correct explanation of statement 1

3. Statement 1 is true and Statement 2 is false

4. Both statements are false

Q.

If two angles of a triangle are ${50}^{\circ }$​ and ${70}^{\circ }$​, then the third angle is:

1. 50^o

2. 120^o

3. 70^o

4. 60^o

Q.

The sum of the three angles of a triangle is $180°$. If the ratio of the angles be $5:6:7$, then find each angle of the triangle.