Question

The sum of the interior angles of a triangle is 180˚, The second angleof a triangle is 45˚ more than the first and the third angle is twice thefirst.

Answer 1

Explanation:

The sum of interior angles of a triangle is

$180^0$

Let the first angle be represented as

$x$

The second angle of a triangle is 45˚ more than the first

This will be represented below as

$x+45$

The third angle is twice the first.

This will be represented below as

$2x$

To figure out the value of the angles, we were given that the sum of angles in the tirangle is 180

Hence,

We will have the expression represented below as

$\begin{gathered} x+(x+45)+2x=180^0 \\ firstangle+secondangle+thirdangle=180^0 \end{gathered}$

By collecting similar terms, we will have

$\begin{gathered} x+(x+45)+2x=180^0 \\ x+x+2x+45=180^0 \\ 4x+45=180^0 \\ substract\text{ 45 from both sides, we will have} \\ 4x+45-45=180-45 \\ 4x=135^0 \\ divide\text{ both sides by 4} \\ \frac{4x}{4}=\frac{135}{4} \\ x=33.75^0 \\ secondangle=x+45=33.75+45=78.75 \\ thirdangle=2x=2\times33.75=67.5^0 \end{gathered}$

Hence,

The final answers are

$\begin{gathered} first\text{ }angle=33.75^0 \\ second\text{ }angle=78.75^0 \\ third\text{ }angle=67.5^0 \end{gathered}$