Question

Given:

[Angle A = 80^°, Angle B = 30^°, m(arc BAC) = 160^° ]

Find:
[m(arc APC) ]
[m(arc AB) ]

a. m(arc APC) = 80^°, m(arc AB) = 30^°
b. m(arc APC) = 50^°, m(arc AB) = 130^°
c. m(arc APC) = 30^°, m(arc AB) = 80^°
d. m(arc APC) = 130^°, m(arc AB) = 50^°

Answer 1

To find arc APC, subtract the measure of arc BAC from 360°. The measure of arc BAC can be found using the angles of triangle ABC.

Step-by-step explanation:

To find the measure of arc APC, we can use the angle of arc BAC and the angles of triangle ABC. In triangle ABC, we know that angle A is 80° and angle B is 30°. Angle C can be found by subtracting angles A and B from 180° (sum of angles in a triangle). So angle C = 180° - 80° - 30° = 70°. Since arc BAC is an inscribed angle that intercepts angle C, its measure is twice the measure of angle C. Therefore, m(arc BAC) = 2 * 70° = 140°.

To find the measure of arc APC, we subtract the measure of arc BAC from 360° (measure of a full circle). So m(arc APC) = 360° - 140° = 220°.

The measure of arc AB is given as 160°.