Question

The angle of a triangle are (2x),(3x+5)and (4x-14). Find the value of x and the measure of each angle of a triangle. What type of triangle it is? ​

Answer 1

QUESTION :-

Find the angles of the triangle and mention which type of triangle it is?

SOLUTION :-

As we know that sum of angles in a triangle is 180°

2x + 3x + 5 + 4x - 14 = 180

9x - 9 = 180

9x = 180 + 9

9x = 189

x = 189/9

x = 21°

1st angle = 2x

= 2(21)

= 42°

2nd angle = 3x + 5

= 3(21) + 5

= 63 + 5

= 68°

3rd angle = 4x - 14

= 4(21) - 14

= 84 - 14

= 70°

Therefore it is a Scalene as all the three angles are different

Answer 2

HELLO DEAR FRIEND

GIVEN IN A TRIANGLE

ANGLES = (2x), (3x+5), (4x-14)

WE KNOW THAT

SUM OF ANGLES OF A TRIANGLE IS

$\large{ {180}^{0} }$

SO,

$\large{2x + 3x + 5 + 4x - 14= {180}^{0} }$

$\large{9x - 9= {180}^{0} }$

$\large{9x = {180} + 9 }$

$\large{9x = 189}$

$\large \bf \it{ x = \frac{ \large{189}}{ \large{9}} }$

$\large \it \bf \boxed{x = 21}$

ANGLES =

$\large{2x}$

$\large{ = 2 \times 21}$

$\large \boxed{ {42}^{0} }$

AND,

$\large{3x + 5}$

$\large{ = (3 \times 21) + 5}$

$= \large{63 + 5}$

$\large \boxed{ {68}^{0} }$

AND,

$\large{4x - 14}$

$\large{(4 \times 21) - 14}$

$\large{84 - 14}$

$\large \boxed{ {70}^{0} }$

SO THE ANGLES ARE,

$\large \boxed{ \boxed {{42}^{0}} \: \boxed{ , {68}^{0}}, \boxed{ {70}^{0} }}$

SINCE IN THIS TRIANGLE ALL ANGLES ARE DIFFERENT SO,

THIS TRIANGLE IS

$\large \boxed{ scalene \: \: \: \: triangle}$

HOPE IT HELPS YOU DEAR FRIEND THANKS