Question

NEED ANSWER ASAP-
What is the value of x?

Answer 1

Given:

The figure.

To find:

The value of x.

Solution:

In triangle HIJ, HJ is diameter of the circle.

`\angle HIJ=90^\circ` [Thales's Theorem]

`HI=IJ` [Given]

`\angle IHJ=\angle IJH=x-42^\circ` [Base angles of isosceles triangles are equal]

Now,

`\angle HIJ+\angle IJH+\angle IHJ=180^\circ` [Angle sum property]

`(90^\circ)+(x-42^\circ)+(x-42^\circ)=180^\circ`

`2x+6^\circ=180^\circ`

`2x=180^\circ-6^\circ`

`2x=174^\circ`

Divide both sides by 2.

`x=(174^\circ)/(2)`

`x=87^\circ`

Therefore, the value of x is
`87^\circ`.