It has a triangle equal to 180 degrees and I don’t understand this, can you help me?

enter image source here

2 Answers
Feb 18, 2018

Answer:

See below.

Explanation:

Here we are formulating an equation to solve for #x#.

We know that the interior angles of any triangle adds up #180# degrees.

We have three angles given:

#60#
#x#
#3x#

This means that :

#60+3x+x=180#

Now we collect like terms to simplify.

#60+4x=180#

Now we solve like any linear equation by isolating the variable on one side of the equation with the constant on the other.

Here we must subtract #60# from both sides to isolate the #x#.

#therefore 60 + 4x -60 = 180 -60#

#=>4x=120#
We want one #x#, therefore we divide by the coefficient of #x# on both sides.

Here we divide by #4#

#4x=120#
#=>x=30#

We can check if we are right by putting our value of #x# back into our formulated equation above.

#60 + (4*30) = 60+120 = 180#

Feb 18, 2018

Answer:

Triangle sum theorem states that all angles in a triangle must add up to #180^@#, a similar theorem applies to quadrilaterals and it states that all angles in a quad. must add up to #360^@#.

Explanation:

You have already applied the triangle sum theorem which states that all 3 angles in a triangle add up to #180# degrees it seems, so now all you have to do is create an algebraic expression that reflects that.

#"Angle 1 + Angle 2 + Angle 3" = 180^@#

#x+3x+60=180#

#4x+60=180#

#4x=120#

So

#x= 30^@#

The angle #x# is 30 degrees and the angle #3x# is #90# degrees