Question

in the given figure alongside, x: y = 2:3 and < ACD = 130०. find the values of x, y and z​

Answer 1

Answer:

the values of x,y and z are 52, 78 and 50 respectively.

Step-by-step explanation:

Given information: x:y = 2:3 and ∠ACD = 130°.

Angle ACB and angle ACD are linear pairs it means they are supplementary angles.

angle ACB+angle ACD=180∠ACB+∠ACD=180

z+130=180z+130=180

z=180-130z=180−130

z=50z=50

It is given that x:y = 2:3.

Let x=2a and y=3a.

angle BAC+angle ABC=(angle) ACD∠BAC+∠ABC=∠ACD (Exterior angle theorem)

3a+2a=1303a+2a=130

5a=1305a=130

Divide both sides by 5.

a=frac{130}{5}a=

5

130

a=26a=26

x=2(26)=52x=2(26)=52

y=3(26)=78y=3(26)=78

Therefore, the values of x,y and z are 52, 78 and 50 respectively.