Question

In ABC, the measure of ZB is thrice to the measure of ZC and the measure of ZA is the sum of the measures of ZB and ZC. Find the measure of all the angles of ABC and also state the type of this triangle,

Answer 1

Step-by-step explanation:

Given:

In ∆ABC , 3∠A= 4∠B= 6∠C

Let x= 3∠A= 4∠B= 6∠C

X=3∠A

∠A= x/3

X=4∠B

∠B= x/4

X=6∠C

∠C= x/6

By angle sum property

∠A+∠B+∠C= 180°

Put the value of ∠A, ∠B, ∠C

X/3+x/4+x/6= 180°

L.c.m of 3,4,6 = 12

(4x + 3x +2x) /12 = 180°

9x = 12 × 180

X= (12× 180) /9

X= 240°

∠A= x/3

∠A= 240/3 = 80°

∠B= x/4

∠B= 240/4= 60°

∠C= x/6

∠C= 240/6 = 40°

_____________________________

Hence the angles be

∠A=80°

∠B=60°

∠C= 40°

_____________________________

Hope this will help you.....

be happy and healthy

Answer 2

$\Uparrow\Uparrow\Uparrow\Uparrow\Uparrow$See the attachment.

$\huge \bigstar$$\huge\bold{\mathtt{\purple{✍︎A{\pink{N{\green{S{\blue{W{\red{E{\orange{R✍︎}}}}}}}}}}}}}$$\huge \Rightarrow$

$\bold \red{Solution:}$

Let ∠B be $\large x°$ and ∠C be $\large y°$.

From the given condition,

$\large \angle A = \angle B + \angle C = (x+y)°$

Also $\Large \frac{x}{y}= \Large\frac {4}{5}$ ∴ $5x=4y$

$\large ∴5x-4y=0$ ...(1)

The sum of the measures of the angles of a triangle is is 180°.

$\large \angle A + \angle B = \angle C=180°$

$\large ∴ (x+y)+x+y=180$

$\large 2x+2y=180$

$\large x+y=90$ ...(2)

Multiplying equation (2) by 4,

$\large 4x+4y=360$ ...(3)

Adding equations (1) and (3),

$\large 5x-4y=0$ ....(1)

$\large \underline 4x+4y =360$ ...(3)

$9x =360$ ∴$x =40$

Substituting$\large x =40$ in equation (2),

$\large40+y=90 \:\:∴y=90-40\:\:\large\\∴y=50$

$\large (x+y)=40+50=90$

$\Large \bold\green{Ans:}\Rightarrow$$\large \angle A =90°,\angle B= 40°\: and \angle C=50°.$