arc qvt measures 156°. which statement must be true? angles qrt and qst both measure 78°. angles qrt and qst…

arc qvt measures 156°. which statement must be true? angles qrt and qst both measure 78°. angles qrt and qst both measure 156°. angle qrt measures 78° and angle qst measures 102°. angle qrt measures 156° and angle qst measures 24°.

arc qvt measures 156°. which statement must be true? angles qrt and qst both measure 78°. angles qrt and qst both measure 156°. angle qrt measures 78° and angle qst measures 102°. angle qrt measures 156° and angle qst measures 24°.

Answer

Answer:

Angles QRT and QST both measure 78°.

Explanation:

Step1: Recall inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc.

Step2: Identify the intercepted arc

The inscribed angles ∠QRT and ∠QST both intercept arc QVT.

Step3: Calculate the measure of the inscribed angles

Given arc QVT = 156°. Using the formula $\text{Inscribed - angle}=\frac{1}{2}\times\text{Intercepted - arc}$, we have $\text{∠QRT}=\text{∠QST}=\frac{1}{2}\times156^{\circ}=78^{\circ}$.