three angles:Triangle

Question

three angles in a triangle always add up to 180 degrees. If one angle in a triangle is 70 degrees and the second is 4 times the third, what are the three angles?

Answer 1

Let's call the three angles: x, y and z

 

We know x= 70 (1)

We know the second angle is 4 times the 3rd angle, so: y = 4*z (2)

We also know that the three angles must add up to 180 degrees: x+y+z=180 (3)

 

We have three equations and three unknowns, so we can solve for the variables. Plugging in eqns (1) and (2) into (3):

 

70 + 4*z + z = 180

5z = 180- 70 = 110

z = 110/5 =22

 

From equation 2, y=4*z = 4* 22 =88

 

 

Checking our answers: 22 + 88 + 70 = 180

Answer 2

First angle = 70

Second angle = 4x

Third angle = x

 

x + 4x + 70 = 180

 

5x + 70 = 180

5x = 110

  x = 22

 

Substitute this value of x into the second and third angle.

Answer 3

A1 + A2 + A3 = 180

 

We know that A1 is 70, so:

 

A2 + A3 = 180 - 70

 

A2 + A3 = 110  <<equation 1>>

 

we also are told that:

A2 = 4*A3

 

sub for A2 in equation 1

4*A3 + A3 = 110

5A3 = 110

A3 = 22

 

and:

A2 = 88

Answer 4

Let a, b, and c be the three angles in the triangle.  Here's what we know:

• a= 70^o
• b = 4c
• a+b+c=180^o

 

Since a = 70^o and b = 4c, let's substitute those values into the third equation:

 

  a    +  b + c = 180^o

70^o + 4c + c = 180^o

70^o + 5c = 180^o

5c = 110^o

 

Can you finish it from here?