Question

. In a triangle ABC, angleB is two-thirds of angleA and angleC is 20° more than angleA. Find the measures of the three
angles of the triangle.
​

Answer 1

Answer:

60°

Step-by-step explanation:

Angle A = x

Angle B = 2x/3

Angle C = x+20°

Sum of all angles of a triangle = 180°

> x + 2x/3 + x+20° = 180°

> 2x/1 + 2x/3 = 180° - 20°

> 6x+2x/3 = 160°

> 8x/3 = 160°

> x = 160°*3/8

> x = 20° * 3

> x = 60°

HOPE YOU UNDERSTAND : THANK YOU

Answer 2

$\huge\purple{\underline{\underline{\pink{Ans}\red{wer:-}}}}$

$\sf{Angle \ A, \ Angle \ B \ and \ Angle \ C}$

$\sf{ are \ 60°, \ 40° \ and \ 80° \ respectively.}$

$\sf\orange{Given:}$

$\sf{\implies{Angle \ B \ is \ two-third \ of \ angle.}}$

$\sf{\implies{Angle \ C \ is \ 20° \ more \ than}}$

$\sf{Angle \ A.}$

$\sf\pink{To \ find:}$

$\sf{Measures \ of \ all \ the \ angles.}$

$\sf\green{\underline{\underline{Solution:}}}$

$\sf{Let \ Angle \ A \ be \ x.}$

$\sf{\therefore{Angle \ B=\frac{2x}{3}}}$

$\sf{\therefore{Angle \ C=x+20}}$

$\sf{Sum \ of \ all \ angles \ of \ triangle \ is \ 180°}$

$\sf{Angle \ A +Angle \ B + Angle \ C=180}$

$\sf{x+\frac{2x}{3}+x+20=180}$

$\sf{Multiply \ both \ sides \ by \ 3 \ throughout}$

$\sf{3x+2x+3x+60=540}$

$\sf{8x=540-60}$

$\sf{8x=480}$

$\sf{x=\frac{480}{8}}$

$\sf{x=60}$

$\sf{\therefore{Angle \ A=60°}}$

$\sf{\therefore{Angle \ B=\frac{2\times60}{3}=40°}}$

$\sf{\therefore{Angle \ C=60+20=80°}}$

$\sf\purple{\tt{\therefore{Angle \ A, \ Angle \ B \ and \ Angle \ C}}}$

$\sf\purple{\tt{are \ 60°, \ 40° \ and \ 80° \ respectively.}}$