Answer:
[tex] x = 39 [/tex]
Step-by-step explanation:
In an inscribed triangle where one of the angles is subtended by a semicircle, that angle is a right angle (90 degrees).
In triangle WXY, angle Y is subtended by the semicircle, so:
[tex] m \angle Y = 90^\circ [/tex]
Now, we're given that:
[tex] m \angle W = (x + 12)^\circ [/tex]
[tex] m \angle X = x^\circ [/tex]
Since the sum of all angles in a triangle is 180 degrees:
[tex] m \angle W + m \angle X + m \angle Y = 180^\circ [/tex]
Substitute the given values:
[tex] (x + 12) + x + 90 = 180 [/tex]
Combine like terms:
[tex] 2x + 102 = 180 [/tex]
Subtract 102 from both sides:
[tex] 2x = 180-102[/tex]
[tex] 2x = 78 [/tex]
Divide by 2:
[tex]x =\dfrac{78}{2}[/tex]
[tex] x = 39 [/tex]
So, the value of x is 39.
