Question

The angles of a triangle are arranged in ascending order of magnitude. If the difference between two consecutive angles is 10°, find all the three angles.

Answer 1

Answer:

the angles of the triangle are 50,60,70

Step-by-step explanation:

given,

the difference between two consecutive angles is 10°, find all the three angles

let the angles be a-10,a,a+10

the sum of the angles in a triangle is 180

so, a-10+a+a+10=180

3a=180

a=60

the angles of the triangle are 50,60,70

Mark me brilliant

Answer 2

☢ Given :

• The difference between two consecutive angles is 10°.

Answer:

Let x , x + 10, x + 20 be the consecutive angles differ by 10°

W K T sum of all angles of triangle is 180°

$\underline{\bigstar\:\textbf{According to the Question :}}$

$:\implies\sf x + x + 10 + x + 20 = 180^{\circ}\\\\\\:\implies\sf 3x + 30 = 180^{\circ}\\\\\\:\implies\sf 3x = 180^{\circ}- 30\\\\\\:\implies\sf x = \dfrac{150^{\circ}}{3}\\\\\\:\implies\sf x = 50^{\circ}\\\\\\\therefore\: \underline{\sf the\:value\: of \:x \:is\: 50^{\circ}.}$

$\underline{\therefore\:\textbf{Required angles are :}}$

$:\implies\sf x\: , x + 10 \:and\: x + 20\\\\\\:\implies\sf x = 50^{\circ}\\\\\\:\implies\sf x + 10 = 50 + 10 = 60^{\circ}\\\\\\:\implies\sf x + 20 = 50 + 20 = 70^{\circ}$

$\therefore\:\underline{\sf{The \:difference\: between\: two\: consecutive\:angles\: is\: 10^{\circ} \:then\: 3 \:angles\: are\: 50^{\circ}\: , 60^{\circ}\: and\: 70^{\circ}}}.$

$\rule{170}{2}$