The value of x is 9. The sum of the two angles m∠THX and m∠XHV equals the angle m∠THV.
What is an angle?
An angle is a corner formed by two rays that end at a common point.
So, the two rays are called the sides of the angle and the endpoint of these two rays is said to be the vertex.
There are three angles: Acute angle, Right angle, and Obtuse angle.
Calculation:
It is given that,
There are three rays [tex]\overrightarrow {HT}[/tex], [tex]\overrightarrow {HX}[/tex], and [tex]\overrightarrow {HV}[/tex]
The angles made by these rays are m∠THV=(12x+18)°, m∠THX=58°, and m∠XHV=(10x−22)°.
The ray [tex]\overrightarrow {HX}[/tex] divides the angle formed by the rays [tex]\overrightarrow {HT}[/tex] , [tex]\overrightarrow {HV}[/tex] into two other angles.
So, we can write,
m∠THV = m∠THX + m∠XHV
⇒ (12x+18)° = 58° + (10x−22)°
⇒ 12x + 18 = 58 + 10x - 22
⇒ 12x -10x = 36 - 18
⇒ 2x = 18
∴ x = 9
Thus, the value of x is 9.
Learn more about an angle here:
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