# The second angle of a triangle is twice the first angle. The third angle is 20 degrees more than the first angle. What is the first angle?

Dec 8, 2015

A1=40

#### Explanation:

Let A1,A2,A3 be the angles of the triangle

We know, A1+A2+A3 = 180 -------(1)
given A2=2(A1) ------(2)
A3= A1+20 --------(3)

Putting 2 & 3 in 1 , we get

A1+2(A1)+A1+20=180

$\implies 4 \left(A 1\right) = 160$

A1=40

Dec 8, 2015

$40$

#### Explanation:

Let x be first interior angle of the triangle. Then, second and third interior angles will be $2 x$ and $x + 20$, respectively.

The sum of the measures of the interior angles of a triangle is 180 degrees:
$\textcolor{w h i t e}{\times} x \textcolor{b l u e}{+} 2 x \textcolor{b l u e}{+} x + 20 = 180$
$\implies 4 x + 20 = 180$
$\implies 4 x + 20 \textcolor{red}{- 20} = 180 \textcolor{red}{- 20}$
$\implies \textcolor{red}{\frac{1}{4} \cdot} 4 x = \textcolor{red}{\frac{1}{4} \cdot} 160$

$\implies x = 40$