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

Feb 18, 2018

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:

$60$
$x$
$3 x$

This means that :

$60 + 3 x + x = 180$

Now we collect like terms to simplify.

$60 + 4 x = 180$

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 $x$.

$\therefore 60 + 4 x - 60 = 180 - 60$

$\implies 4 x = 120$
We want one $x$, therefore we divide by the coefficient of $x$ on both sides.

Here we divide by $4$

$4 x = 120$
$\implies x = 30$

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

$60 + \left(4 \cdot 30\right) = 60 + 120 = 180$

Feb 18, 2018

Triangle sum theorem states that all angles in a triangle must add up to ${180}^{\circ}$, a similar theorem applies to quadrilaterals and it states that all angles in a quad. must add up to ${360}^{\circ}$.

#### 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.

$\text{Angle 1 + Angle 2 + Angle 3} = {180}^{\circ}$

$x + 3 x + 60 = 180$

$4 x + 60 = 180$

$4 x = 120$

So

$x = {30}^{\circ}$

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