what is m∠t? m∠t =

Explanation:

Step1: Use the property of inscribed - angles

In a circle, inscribed angles that intercept the same arc are equal. $\angle S$ and $\angle T$ intercept the same arc $\overset{\frown}{RQ}$, so $m\angle S=m\angle T$.

Step2: Set up an equation

We know that $m\angle S = 10x + 22^{\circ}$ and $m\angle T=2x + 38^{\circ}$. Since $m\angle S=m\angle T$, we have the equation $10x + 22=2x+38$.

Step3: Solve the equation for $x$

Subtract $2x$ from both sides: $10x-2x + 22=2x-2x + 38$, which simplifies to $8x+22 = 38$. Then subtract 22 from both sides: $8x+22 - 22=38 - 22$, getting $8x=16$. Divide both sides by 8: $x=\frac{16}{8}=2$.

Step4: Find $m\angle T$

Substitute $x = 2$ into the expression for $m\angle T$. $m\angle T=2x + 38^{\circ}$. So $m\angle T=2\times2+38^{\circ}=4 + 38^{\circ}=42^{\circ}$.

Answer:

$42$