Angle Sum Property of a Triangle

Q. Question 108
State whether the statements are True or False.
The interior angles of a triangle are in the ratio 1 : 2 : 3, then the ratio of its exterior angles is 3 : 2 : 1.

Q.

In the given figure, ABCD is a quadrilateral and AO and DO are bisectors of $\angle Aand\angle D$. The value of 'x ' is

1. 
2. 
3. 
4. 

Q. Find the angles of quadrilateral ABCD, in given figure.

Q. The measure of ∠x in the given figure is .

1. ${120}^o$
2. ${100}^o$
3. ${90}^o$
4. ${110}^o$

Q. Question 159
ABCDE is a regular pentagon. The bisector of angle A meets the sides CD at M. Find $\angle AMC$

Q. In the given figure, ABCD is a quadrilateral and $\angle ADC=a^{\circ },\angle BCD=b^{\circ }.$ AO and BO are bisectors of $\angle DAB$ and $\angle ABC$ respectively meeting at O. Find $\angle AOB$ in terms of $a^{\circ }$ and $b^{\circ }$.

1. $a+b$
2. $\frac{(a+2b)}{2}$
3. $\frac{a+b}{2}$
4. $(a+2b)\times 2$

Q. If the interior angles of a triangle are in the ratio 2 : 3 : 5, find the smallest interior angle of the triangle.

1. 60°
2. 90°
3. 36°
4. 72°

Q. In isosceles triangle ABC, AB = AC. The side BA is produced to D such that BA = AD.
Is $\angle BCD={90}^{\circ }$. ?
If true then enter 1 else if False enter 0

Q. In the given figure
$\angle A+\angle B+\angle C+\angle D+\angle E$ is equal to

1. $\frac{\pi }{2}$
2. $\pi$
3. $\frac{3\pi }{2}$
4. $2\pi$

Q. In a rhombus $ABCD,\angle CBA={40}^{\circ }$.
Find the other angles.

Q. Find the angles of quadrilateral ABCD, in given figure.

Q. Construct an equilateral triangle $\Delta ABC$. Construct an angle bisector of $\angle A$.
Let it meet side $BC$ at $D$. Find measures of $BD$, and $DC$. Then:

1. $BD>CD$
2. $BD=CD$
3. $BD<CD$
4. None

Q. The measures of angles of a triangle are in the ratio $1:2:3$. Determine the measures of smallest angle of the triangle.

Q. In the given figure, ABCD is a quadrilateral and $\angle ADC=a^{\circ },\angle BCD=b^{\circ }.$ AO and BO are bisectors of $\angle DAB$ and $\angle ABC$ respectively meeting at O. Find $\angle AOB$ in terms of $a^{\circ }$ and $b^{\circ }$.

1. $a+b$
2. $\frac{(a+2b)}{2}$
3. $\frac{a+b}{2}$
4. $(a+2b)\times 2$

Q. It is given that $\Delta DEF\sim \Delta RPQ$. Is it true to say that $\angle D=\angle Rand\angle F=\angle P?$ why?

Q. The measure of $\angle BAC$ is

1. ${50}^{\circ }$
2. ${65}^{\circ }$
3. ${55}^{\circ }$
4. ${60}^{\circ }$

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

Q. WXYZ is a parallelogram. Find the angle XYP (in degrees).

1. 135

Q. In the figure given below, $LM=LN$; angle $PLN={110}^o$.
Calculate:
$\angle MLN$

Q. In $△ABC$, $AB=AC$ and $\angle A={36}^{\circ }$. If the internal bisector of $\angle C$ meets AB at point D, then:

1. $AD=BC$
2. $AD=AC$
3. $AD=AB$
4. $AB=AC=BC$

Q. In parallelogram $ABCD$, the bisector of angle $A$ meets $DC$ at $P$ and $AB=2AD$.
Prove that:
(i) $BP$ bisects angle $B$.
(ii)Angle $APB={90}^o$.

Q.

1. ${90}^{\circ }$
2. ${20}^{\circ }$
3. ${60}^{\circ }$
4. ${40}^{\circ }$