Question

directions: use this information to answer parts a and b. an inscribed angle with a diameter as a side has a measure of (x^{circ}). part a if the ratio of (moverparen{cd}) to (moverparen{db}) is (1:3), what is (moverparen{db})? enter the correct value in the box. show hints

Explanation:

Step1: Recall circle - arc property

The sum of the measures of arcs $\overparen{CD}$ and $\overparen{DB}$ is $180^{\circ}$ since $\angle CBD$ is an inscribed - angle with a diameter as a side, and an inscribed angle with a diameter as a side is a right - angle, and the arc it intercepts is a semi - circle.

Step2: Set up ratio equation

Let the measure of $\overparen{CD}=x$ and the measure of $\overparen{DB}=3x$ (since the ratio of $\overparen{CD}$ to $\overparen{DB}$ is $1:3$). Then $x + 3x=180^{\circ}$.

Step3: Solve the equation

Combining like terms, we get $4x = 180^{\circ}$. Dividing both sides by 4, $x=\frac{180^{\circ}}{4}=45^{\circ}$.

Step4: Find the measure of $\overparen{DB}$

Since the measure of $\overparen{DB}=3x$, substituting $x = 45^{\circ}$, we have $m\overparen{DB}=3\times45^{\circ}=135^{\circ}$.

Answer:

$135$