Question

Select the correct answer from each drop-down menu. B For circle O, m In the figure, 2 C CD T - 125° and m2ABC= 55°. and 2 have measures equal to 35°.​

Answer 1

Explanation:

The relevant relations here are ...

• the sum of arc measures in a semicircle is 180°
• the sum of angles in a triangle is 180°

Arc measures

The given arc CD is part of the semicircular arc CDA. The remaining arc, DA, is the supplement of CD:

arc DA = 180° -CD = 180° -125° = 55°

Central angle AOD has the same measure, 55°. That is one of the acute angles in right triangle AOB, so the other one is the complement of 55°.

∠ABO = 90° -∠AOB = 90° -55°

∠ABO = 35°

Triangle angles

In right triangle ABC, angle ABC is given as 55°. The other acute angle, ACB, will be the complement of this.

∠ACB = 90° -∠ABC = 90° -55°

∠ACB = 35°

In the figure, angles ABO and ACB have measures of 35°.