Can you solve this under a minute?

Geometry Level 1

The angles of a triangle are $a$ , $b$ and $50 ^ \circ$ .

If the difference $a - b$ is $40 ^ \circ$ , then what is the value of $a$ ?

{ 90 }^{ o }

{ 68 }^{ o }

{ 75 }^{ o }

{ 85 }^{ o }

15 solutions

Heder Oliveira Dias
Jul 28, 2014

If the first angle is 50º, then the a plus b are 130º, because the sum of internal angles are 180º and 50º + a + b = 180, then a + b = 180 - 50, a + b = 130º. Hence, the difference between the a and b is 40º, then a - b = 40. We solve the system a + b = 130, a - b = 40, and we have... 2a = 170,
a = 85º . Thus a = 85º.

gilgit baltistan a-b=40
a=40+b sum of all interior angles of a triangle is equal to 180 a+b+50=180 by putting the value of a 40+b+b+50=180 2b+90=180 b=45 now a=40+45 a=85

Asif Ali - 6 years, 10 months ago

b-a can also be equal to 40 why should i take a-b =40

Abhishek Sonu - 6 years ago

a+b+50=180 a-b=40 (let, a>b) adding these 2 eqns 2a+50=180+40 2a=170 therefore, a=85 & b=85-40=45...

Arif Rahman - 6 years, 10 months ago

a+b+50= 180 a+b= 180-50= 130 a-b= 40 a+b+a-b = a+a= 2a = 130 + 40 = 170 2a = 170 a=170/2 a= 85 Now, a-b = 40 85 - b = 40 -b = 40-85 -b= -35 OR b = 35 35 + 85 + 50 = 170, but it should be 180

Minhal Shafique - 6 years, 10 months ago

Ahmad Hesham
Jul 30, 2014

From the given information we know that : $a-b=40°\quad (1)$

& the sum of internal angles of any triangle is 180° so we have : $a+b+50=180°\\ a+b=130°\quad (2)\\ \\ \\ \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad a-b=40°\quad (1)\\ \quad \quad \quad \quad \quad \quad \quad \quad \quad +\\ \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad a+b=130°\quad (2)\\ \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad 2a=170°\\ \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \boxed { a=85° }$

sum of angle in Triangle is 180° therefore a+b+c=180°--------1 a-b=40° (given) or a=40°+b-------------2

put the value in equation 1 we get 40°+b+b+c=180 C=50° (given) we get 2b+90°=180° 2b =180°-90 b=45° put the value of b in equation 2 from that a=85°

40+

baljeet kumar - 6 years, 10 months ago

Nishant Singh
Jul 30, 2014

Simple a - b = 40 (Given) i.e. b = a - 40

3rd angle = 50 (Given)

Formula = sum of angles of triangle = 180

i.e. a + b + 50 = 180

a + a - 40 + 50 = 180

2a = 170

a = 85

a + b + 50 = 180 a - b = 40 a = b + 40 b + 40 + b + 50 = 180 2b = 90 b = 45 a + 45 + 50 = 180 a = 180 - 95 a = 85

Chelo Pablo-Norico - 6 years, 10 months ago

a + b + 50 = 180

a - b = 40

a = b + 40

b + 40 + b + 50 = 180

2b + 90 = 180

2b = 90

b = 45

a + 45 + 50 = 180

a = 180 - 95

a = 85

Chelo Pablo-Norico - 6 years, 10 months ago

so we have a+b+50=180 a-b=40 simple steps... and... a=85 :)

Guillermo Chan - 6 years, 10 months ago

Arif Rahman
Jun 15, 2015

a+b+50=180....(1)

a~b=40

let, a>b then, a-b=40....(2) adding these 2 eqns 2a+50=180+40 or, 2a=170 therefore, a=85 & b=85-40=45...

if b>a then, b-a=40.....(3)

subtracting (3) from (1) a+b+50-b+a=140 or, 2a = 90 or, a = 45

A Former Brilliant Member
Dec 15, 2014

the sum of internal angles are 180. so: a+b+50=180 then a+b=130 and a-b=40 so if we solve that we reach to a=85.

Akhil Vuriti
Nov 17, 2014

f the first angle is 50º, then the a plus b are 130º, because the sum of internal angles are 180º and 50º + a + b = 180, then a + b = 180 - 50, a + b = 130º. Hence, the difference between the a and b is 40º, then a - b = 40. We solve the system a + b = 130, a - b = 40, and we have... 2a = 170, a = 85º . Thus a = 85

Vinit Béléy
Sep 26, 2014

Sum of all angles is 180˚ a + b + 50˚ = 180˚

Since |b - a| = 40 a + (a - 40˚) + 50˚ = 180˚

2a + 10˚ = 180˚

a = 170˚/2 = 85˚

Karim Shaféiq
Sep 15, 2014

there is 2 Unknown values & 2 equations

a+b+50=180

a-b=40

solve 2 equ.. a=85 , b=45

Karl Anthony Baluyot
Aug 30, 2014

a - b = 40, so a = 40+b. From the law of triangles, a+b+50=180. Substituting a we get, 40+b+b+50 = 180. 2b+90=180. 2b=180-90. b=45. Going back from equation 2, a = 40+b, a = 40 + (45) , a = 85.

Muhammad Ibraheem
Aug 2, 2014

solving a+b+50=180 and a-b=40 equations simultaneously gives a=85

Meena Sharma
Aug 1, 2014

a+b+50=180 then a+b=130 -----(1) &given a-b=40 -----(2) from (1) & (2),we get a=85

Chun Yee Goh
Jul 31, 2014

same here use 180 minus 50 u will get 130. If the difference is 40, use (130-40)^2 and you will get 45. Then use 45+40 equals 85

Anil Saini
Jul 31, 2014

we know a+b+c=180 degree , given c=50 , a-b=40 . b=a-40 ,Hence a+a-40+50=180 , a=85

Abu Jubaer
Jul 31, 2014

As we know that the sum of the 3 angels of a triangle is 180º. So, a+b+50º=180º. Then, a+b=130º Hence, the difference between a & b given, then a-b=40º Now, if we add these 2 equations, we have 2a=170º. Which gives us a=85º

[If asked for the value of b] If we deduct 2nd equation from 1st equation, then (a+b)-(a-b)=130º-40º a+b-a+b=90º 2b=90º So, b=45º

Amanpreet Singh
Jul 31, 2014

Simple a - b = 40 (Given) i.e. b = a - 40 3rd angle = 50 (Given) Formula = sum of angles of triangle = 180 i.e. a + b + 50 = 180 a + a - 40 + 50 = 180 2a = 170 a = 85

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