NEED ANSWER ASAP- What is the value of x?

Question

asked May 7, 2021 113k views

1 Answer

MikeRalphson · Answer 1 · 2021-05-12T15:30:51+0000

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
$87^\circ$ .