In Triangle ABC, ∠A is 10 degrees greater than ∠B, and ∠B is 10 degree

Question

In Triangle ABC, ∠A is 10 degrees greater than ∠B, and ∠B is 10 degrees greater than ∠C. The value of angle B is

(A) 30 
(B) 40 
(C) 50 
(D) 60 
(E) 70

Source:   Nova GMAT  
Difficulty Level:   550

sashiim20 · Answer

Let  ∠C = x

∠B = x + 10

∠A = x + 10 + 10 = x + 20

∠A + ∠B + ∠C = 180

x + 20 + x + 10 + x = 180

3x + 30 = 180

3x = 180 - 30 = 150

x = 150/3 = 50

∠C = 50

∠B =x + 10 = 50 + 10 = 60  . Answer (D) ...

generis · Answer

Define all angles in terms of ∠B (= b, ∠A = a, ∠C = c).

a = b + 10 
 
b = c + 10, or

c = b - 10

a + b + c = 180, substitute values in bold type

(b + 10) + b + (b - 10) = 180

3b = 180

b = 60
Answer  D

pushpitkc · Answer

The sum of all the angles in a triangle is 180 Degree.
If the three angles have to differ by 10 and add to 180, 
 the only possibility(with a difference of 10) is when the three angles are 50,60 and 70.
 
Since ∠B is 10 degree greater than ∠C and 10 degree smaller than ∠A,  it must be 60(Option D)

harikrish · Answer

In Triangle ABC, ∠A is 10 degrees greater than ∠B, and ∠B is 10 degrees greater than ∠C. The value of angle B is

(A) 30 
(B) 40 
(C) 50 
(D) 60 
(E) 70

Solution:
Given:
a=b+10
b=c+10
Also, we know
a+b+c=180.----eq (1)

Therfore subsitute the value of a and c in the eq(1)
we ger 
b+10+b+b-10=180.
3b=180.
b=60.

So Option D

chetan2u · Answer

Hi,

Here actually difference of 10 doesn't matter. Any difference but similar would give us SAME answer as 60.. WHY?

The three angles differ by certain amount so they are in AP and central angle B would be the MEAN 
So 3*B =180..... B=60
D

amanvermagmat · Answer

If all three angles are equal: 60, 60, 60

If the three angles are in Arithmetic Progression with a difference of 10: 50, 60, 70

So the central angle is 60 only. Hence  D answer

shashankism · Answer

Let the /_C = x
So, /_ B = x +10
/_ A = x +20

A + B + C = x+20 + x +10 +x = 180 
-> 3x +30 = 180 
-> x= 150/3 = 50

So, /_B = 50 +10 = 60

Answer D

Abhishek009 · Answer

Let the value of  ∠A = a°  ,  ∠B = b°  and  ∠C = c°

We know,  ∠A + ∠B + ∠C = 180°  Or,  a° + b° + c° = 180°

Value of  ∠B  =  ( c° + 10° ) 
Value of  ∠A  =  ( b° + 10° )  =>  ( c° + 10° ) + 10°  =  c° + 20° 
Value of  ∠C  = c°

Now,  (c° + 20°)  +  ( c° + 10° )  +  c°  =  180°

Or,  3c° + 30° = 180°

Or,  3c° = 150°

So, c° = 50°

Now, as Value of  ∠B  =  ( c° + 10° )  =  60°

Thus, answer will be (D) 60°

JeffTargetTestPrep · Answer

We can let angle C = x, angle B = 10 + x, and angle A = 20 + x. Since there are 180 degrees in a triangle, we have:
 
x + x + 10 + x + 20 = 180
 
3x + 30 = 180
 
3x = 150
 
x = 50
 
Thus, angle B is 50 + 10 = 60 degrees.
 
Answer: D

arvind910619 · Answer

IMO D 
A+B+C=180
B+10+B+B-10=180
3B=180
B=60

mamun2871 · Answer

Here,A=C+10+10 =>A=C+20 Hence, C+20+C+10+C=180 C=150/3=50 Therefore, B=50+10=60 Answer: D

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In Triangle ABC, ∠A is 10 degrees greater than ∠B, and ∠B is 10 degree

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