Question

what is the value of x? 37° 14x - 73°

Explanation:

Step1: Recall circle - angle property

In a circle, if an arc is subtended by an inscribed - angle, and the arc is a semi - circle, the inscribed - angle is a right angle. In triangle $VTU$, since $VU$ is a diameter of the circle, $\angle{VTU}=90^{\circ}$. The sum of the interior angles of a triangle is $180^{\circ}$. So, $\angle{TVU}+\angle{UTV}+\angle{TUV}=180^{\circ}$. Given $\angle{TVU} = 37^{\circ}$ and $\angle{TUV}=14x - 73^{\circ}$ and $\angle{UTV}=90^{\circ}$, we can write the equation: $37+(14x - 73)+90 = 180$.

Step2: Simplify the left - hand side of the equation

First, combine like terms: $37-73 + 90+14x=180$. $(37 + 90-73)+14x=180$. $(127 - 73)+14x=180$. $54+14x=180$.

Step3: Solve for $x$

Subtract 54 from both sides of the equation: $14x=180 - 54$. $14x=126$. Then divide both sides by 14: $x=\frac{126}{14}=9$.

Answer:

$9$