Question

7 numeric 1 point if arc bc = (9x - 53)° and arc cd = (2x + 45)°, find arc bad. answer

Explanation:

Step1: Use the property of congruent arcs

Since the chords are equidistant from the center, arc \(BC = arc\ CD\). So, \(9x - 53=2x + 45\).

Step2: Solve the equation for \(x\)

Subtract \(2x\) from both sides: \(9x-2x - 53=2x-2x + 45\), which gives \(7x-53 = 45\).
Add \(53\) to both sides: \(7x-53 + 53=45 + 53\), so \(7x=98\).
Divide both sides by \(7\): \(x=\frac{98}{7}=14\).

Step3: Find the measure of arc \(BC\) and \(CD\)

Substitute \(x = 14\) into \(9x-53\): \(9\times14-53=126 - 53=73^{\circ}\). So arc \(BC=arc\ CD = 73^{\circ}\).

Step4: Calculate arc \(BAD\)

The sum of arcs in a circle is \(360^{\circ}\). Arc \(BAD=360-(73 + 73)\).
\(arc\ BAD=360 - 146=214^{\circ}\).

Answer:

\(214\)