Congruent Triangles

Q. If in a triangle ABC, angle A+ angle B = 105° and angle B + angle C= 120°, then angle B is?

My attempt -

Angle A + Angle B = 105° ..... (1)

Angle B + Angle C = 120°
or Angle C = 120° – Angle B ........ (2)

Now, Angle A + Angle B + Angle C = 180° (Angle Sum property of a triangle)
or 105° + 120° - Angle B = 180° (Substituting values from (1) and (2))
or 225° - Angle B = 180°
or Angle B = 225° – 180° = 45°

I am doubtful of my solution. Can you please help me determine if I've solved it the correct way? I know it's a simple question, still silly doubts. Thanks!

Q.

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

1. 60^o, 40^o, 80^o

2. 20^o, 60^o, 80^o

3. 40^o, 60^o, 80^o

4. 80^o, 40^o, 60^o

Q.

Q.

In a triangle ABC, angle A- angle B=33degree and angle B- angle C=18 degree, then the measure of angle B is?

Q.

In figure, QA and PB are perpendicular to AB. If AO = 10cm, BO = 6cm and PB = 9cm.
Find AQ.

Q.

Two triangles ABC and DEF are such that, AB = ED, BC = DF, AC = EF

1. 

2. 

3. 

4. 

Q.

D, E, F are the mid-point of the sides BC, CA and AB respectively of $\Delta ABC,then\Delta DEF$ is congruent to triangle

1. AEF

2. AFE, BFD, CDE

3. ABC

4. BFD, CDE

Q.

The angles of a triangle are in the ratio 2: 3: 4; the three angles are

1. 40^o, 60^o, 80^o

2. 70^o, 46^o, 64^o

3. 80^o, 50^o, 50^o

4. 60^o, 90^o, 30^o

Q.

In the figure, the measure of $\angle B^{\prime }{A}^{\prime }{C}^{\prime }$ is

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

2. ${60}^{\circ }$

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

4. ${80}^{\circ }$

Q.

If $\Delta PQR\cong \Delta EFD,thenED=$

1. PQ

2. QR

3. None of these

4. PR

Q.

If ABC and DEF are two triangles such that $\Delta ABC\cong \Delta FDEandAB=5cm,\angle B={40}^{\circ }and\angle A={80}^{\circ }.$ Then, which of the following is true?

1. DF = 5 cm, $\angle F={60}^{\circ }$

2. DE = 5 cm, $\angle D={40}^{\circ }$

3. DE = 5 cm, $\angle E={60}^{\circ }$

4. DF = 5 cm, $\angle E={60}^{\circ }$

Q.

If one angle of a triangle is 120°, then find the angle between the bisectors of the other two angles.

Q.

In two congruent triangles ABC and DEF, if AB = DE and BC = EF. Name the pairs of equal angles.

Q.

In $\Delta ABC\cong \Delta LKM,\text{then side of}\Delta LKM\text{equal to side AC of}\Delta ABCis$

1. LK

2. KM

3. LM

4. None of these

Q. Define an axiom?

Q.

If the angle of a triangle is in ratio 1:2:3, find the measure of the smallest angle.

Q.

One of the angles of a triangle is $100°$ and other two angles are equal. Find each of the equal angles.

Q.

If $\Delta ABC\cong \Delta PQR$ and it is given that $\angle A={60}^{\circ },\angle B={70}^{\circ }.$Then the value of $\angle R$ is___.

Q. If ∆ABC ≅ ∆ PQR and ∆ABC is not congruent to ∆RPQ, then BC = PQ

1. False
2. True

Q.

If $\Delta ABC\cong \Delta PQRand\Delta ABC\text{is not congruent to}\Delta RPQ,\text{then which of the following is not true:}$

1. BC = PQ

2. AC = PR

3. AB = PQ

4. QR = BC

Q.

If $\Delta DEF\cong \Delta BCA$ , then the angle of $\Delta BCA$ that corresponds to $\angle E$ is _______ and side $FD$ corresponds to side ________.

1. $\angle A$, $BC$

2. $\angle B$, $AB$

3. $\angle C$, $AB$

4. Both $\angle C$​ and $\angle A$​, $BC$

Q.

The angles of a triangle are in the ratio 1:2:3, find the measure of each angle of the triangle

Q.

In $\Delta ABC\cong \Delta ACB,then\Delta ABC$ is isosceles with

1. AB = BC

2. AB = AC

3. AC = BC

4. None of these

Q. In a Δ ABC, if ∠A = 55°, ∠B = 40°, find ∠C.

Q. If triangles PQR and ABC are congruent, then the angle(s) of triangle PQR that corresponds to angle C is/are

1. $\angle P$
2. $\angle Q$
3. $\angle R$
4. $\angle P,\angle Q\text{and}\angle R$

Q. Question 7
It is given that $\Delta ABC\cong \Delta FDE$ and AB =5 cm, $\angle B={40}^{\circ }and\angle A={80}^{\circ }$, then which of the following is true?
(A) DF = 5 cm. $\angle F={60}^{\circ }$
(B) DF = 5 cm. $\angle E={60}^{\circ }$
(C) DE = 5 cm. $\angle E={60}^{\circ }$​​​​​​​
(D) DE = 5 cm. $\angle D={60}^{\circ }$​​​​​​​

Q.

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

1. 93^o

2. 46^o

3. 73^o

4. 83^o

Q.

If three sides of a triangle are equal to the corresponding three sides of another triangle, named in sequence, then the two triangles are said to be __ triangles.

Q.

In the figure below, $△$ABC $\cong$ $△$BED, $\angle$DEB = ${115}^{\circ }$ and $\angle$CAB = ${25}^{\circ }$. It can be concluded that BC||ED.

1. 

2. 

Q.

The diagonal PR of a quadrilateral PQRS bisects the angles P and R, then

1. PS = PQ and QR = RS

2. PS = PR and SR = QS

3. PS = RS and PQ = QR

4. PQ = SR and QR = PS