## Related questions with answers

Question

Find all interior angles of a triangle, using the given the ratios among them. Angles' ratio: 3:4:5

Solution

VerifiedStep 1

1 of 2Using the extended ratio, we can let the angles be $3x$, $4x$, and $5x$, all in degrees.

By Triangle Sum Theorem, the sum of the interior angle measures in a triangle is $180\text{\textdegree}$ so we can write:

$3x+4x+5x=180\text{\textdegree}$

Solve for $x$:

$12x=180\text{\textdegree}$

$x=15\text{\textdegree}$

So, the measures of the interior angles are:

$\begin{align*} 3x&\to 3(15\text{\textdegree})=\color{#c34632}45\text{\textdegree}\\ 4x&\to 4(15\text{\textdegree})=\color{#c34632}60\text{\textdegree}\\ 5x&\to 5(15\text{\textdegree})=\color{#c34632}75\text{\textdegree} \end{align*}$

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