Question

abcd is inscribed in circle o. the paragraph explains why ∠adc is supplementary to ∠abc. which is the statement that correctly completes the paragraph? ∠adc and ∠abc are inscribed angles in circle o. the measure of ∠adc is half the measure of arc abc and the measure of ____________. arcs abc and cda make up the whole circle, or 360°. so, the sum of the measures of ∠adc and ∠abc must be half of 360°, or 180°.

Explanation:

Inscribed angles subtend arcs; the measure of an inscribed angle is half its subtended arc. ∠ADC subtends arc ABC, so ∠ADC = ½ arc ABC. ∠ABC must subtend the complementary arc CDA for their sum to be ½(arc ABC + arc CDA) = ½(360°) = 180°. Thus, ∠ABC is half the measure of arc CDA.

Answer:

∠ABC is half the measure of arc CDA