Question

The angles of a triangle are (3x)°; (2x + 60)° and (5x – 40)°.
then The measure of the largest angle is ​

Answer 1

Step-by-step explanation:

3x+2x+60+5x-40=180°

10x+20=180

10x=160

x=16

angle:48°,92°,40°

largest angle is 92°

Answer 2

The angles of a triangle :-

= (3x)°

= (2x + 60)°

= (5x - 40 )°

Then, according to the angle sum property :-

$= \texttt{3}x + \texttt{2}x + \: \texttt{60} \: + \texttt{5}x \texttt{ \: - 40 \: = 180} \:$

$= \texttt{3}x + \texttt{2}x + \texttt{5}x + \texttt{60 + (- 40)} \texttt{ \: = 180}$

$= \texttt{10}x \texttt{ \: + 20 \: = \: 180}$

$= \texttt{10}x \: \texttt{ = 180 - 20}$

$= \texttt{10}x \: \texttt{ = 160}$

$= x = \frac{\texttt{160}}{\texttt{10} }$

$= x \texttt{ \: = 16}$

Using this value of x, let us find out the value of each angle :-

$\texttt{(i)∠ \:3}x$

$= \texttt{3 × 16}$

$= \color{olive}\texttt{∠3}\color{olive}x \: = \color{hotpink}\: \texttt{48}°$

$\texttt{(ii)} \: \texttt{∠2x \: + \: 60 \: = }$

$= \texttt{(2 \: × \: 16 \: ) + 60}$

$= \color{olive}\texttt{∠2x \: + \: 60 \: = \color{hotpink}}\color{hotpink}\texttt{92}°$

$\texttt{(iii)∠5}x \: \texttt{ \: - 40 }$

$= \texttt{5 \: × \: 16 \: - 40}$

$\color{olive} \texttt{∠5}x \: \texttt{ \: - 40 }=\color{hotpink} \: \texttt{40}°$

As the sum of all the angles is adding upto 180° (48+92+40=180), we can conclude that we have found out the correct value of x and the angles of this triangle.

Therefore, the measure of the largest angle = 92°