Question

Given: ∠ A = 80° , ∠ B = 30° , m(textarc BAC) = 160°

Find: m(textarc APC) and m(textarc AB) .

a) m(textarc APC) = 50° , m(textarc AB) = 110°
b) m(textarc APC) = 110° , m(textarc AB) = 50°
c) m(textarc APC) = 80° , m(textarc AB) = 30°
d) m(textarc APC) = 30° , m(textarc AB) = 80°

Answer 1

To find the measure of arc APC, subtract the measure of angle B from 180° and then multiply by 2. To find the measure of arc AB, subtract the measure of arc APC from 360°.

Step-by-step explanation:

To find the measure of arc APC, we can use the fact that the sum of the measures of angles at a point on a circle is 360°. Since ∠B = 30° and m(arc BAC) = 160°, we can find the measure of ∠BAC by subtracting ∠B from 180° (since ∠BAC is an exterior angle of ∆ABC). Therefore, ∠BAC = 180° - 30° = 150°. Since ∠BAC is an inscribed angle that intercepts arc APC, the measure of arc APC is twice the measure of ∠BAC, which is 2 * 150° = 300°.

To find the measure of arc AB, we can subtract the measure of arc APC from the measure of the entire circle, which is 360°. Therefore, m(arc AB) = 360° - 300° = 60°.