Question

The angles of a triangle are in the ratio 3:1:2. Find the measure of the largest angle
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Answer 1

3x+x+2x=180°{angle sum property of triangle}

6x=180

x=30

3x=3×30=90

2x=2×30=60

largest angle is 90°.

Answer 2

Given :-

The ratio of the angle measures of a triangle = 3:1:2

The sum of all three of these angles = 180°(angle sum property)

Then :-

Total number of parts = 3+1+2 = 6

Measure of the first angle :-

$= \frac{\texttt{3}}{\texttt{6}} \: \texttt{ \: of \: 180}$

$= \frac{\texttt{3}}{\texttt{6}} \texttt{ \: × \: 180}$

$= \frac{\texttt{3×180}}{\texttt{6} }$

$= \frac{\texttt{540}}{\texttt{6} }$

$= \texttt{\color{hotpink}90}\color{hotpink}°$

So, the measure of the first angle = 90°

Measure of the second angle :-

$= \frac{\texttt{1}}{\texttt{6}} \: \texttt{ of \: 180}$

$= \frac{\texttt{1}}{\texttt{6}} \texttt{ \: × \: 180}$

$= \frac{\texttt{1×180}}{\texttt{6} }$

$= \frac{\texttt{180}}{\texttt{6} }$

$= \texttt{\color{hotpink}30}°$

So, the measure of the second angle = 30°

Measure of the third angle :-

$= \frac{\texttt{2}}{\texttt{6}} \: \texttt{ \: of \: 180}$

$= \frac{\texttt{2}}{\texttt{6}} \texttt{ \: × \: 180}$

$= \frac{\texttt{2×180}}{\texttt{6} }$

$= \frac{\texttt{360}}{\texttt{6} }$

$=\texttt{\color{hotpink}60}°$

The measure of the third angle = 60°

As the measure of all three angles of this triangle is adding upto 180°(90+30+60=180), we can conclude that we have found out the correct measure of each of the angles.

Therefore, the measure of the largest angle = 90°