Question

ور)
The angles of atriangle
are 3x+12, 5x-6
and x + 3 then measure of angle is​

Answer 1

3x+12 + 5x-6 + x+3 = 180°

9x + 9 = 180°

9(x+1) = 180°

x = 19

angle 1 = 69°

angle 2 = 89°

angle 3 = 22°

Answer 2

Answer

We know that,

${\sf \dashrightarrow {Sum \: of \: all \: angles}_{Triangle} = {180}^{\circ}}$

${\sf \dashrightarrow (3x + 12) + (5x - 6) + (x + 3) = {180}^{\circ}}$

${\sf \dashrightarrow 9x + 6 + 3 = {180}^{\circ}}$

${\sf \dashrightarrow 9x + 9 = {180}^{\circ}}$

${\sf \dashrightarrow 9x = 180 - 9}$

${\sf \dashrightarrow 9x = 171}$

${\sf \dashrightarrow x = \dfrac{171}{9}}$

${\sf \dashrightarrow x = 19}$

Now, we can find the measurement of each angle of the triangle by using the given measurements of angles given to us in variable format.

First angle of triangle :

${\sf \dashrightarrow 3x + 12}$

${\sf \dashrightarrow 3(19) + 12}$

${\sf \dashrightarrow 57 + 12 = {69}^{\circ}}$

Second angle of triangle :

${\sf \dashrightarrow 5x - 6}$

${\sf \dashrightarrow 5(19) - 6}$

${\sf \dashrightarrow 95 - 6 = {89}^{\circ}}$

Third angle of triangle :

${\sf \dashrightarrow x + 3}$

${\sf \dashrightarrow 19 + 3 = {22}^{\circ}}$

Hence, the three angles of the triangles measure 69°, 89° and 22° respectively.