what is the measure of arc bec in circle d? 134° 150° 209° 210°
what is the measure of arc bec in circle d? 134° 150° 209° 210°
Answer
Answer:
D. 210°
Explanation:
Step1: Find measure of arc BC
The measure of an inscribed - angle is half the measure of its intercepted arc. In (\triangle ABC), (\angle BAC = 76^{\circ}) and (\angle ABC=75^{\circ}). First, find (\angle ACB) using the angle - sum property of a triangle ((\angle A+\angle B+\angle C = 180^{\circ})). So, (\angle ACB=180-(76 + 75)=29^{\circ}). The inscribed angle (\angle BAC) intercepts arc (BC), and by the inscribed - angle theorem, if (\angle BAC = 76^{\circ}), then the measure of arc (BC = 2\times\angle BAC=152^{\circ}).
Step2: Find measure of arc BEC
The sum of the measures of the arcs of a circle is (360^{\circ}). Let the measure of arc (BEC) be (x) and the measure of arc (BC) be (y). We know that (x + y=360^{\circ}). Since (y = 150^{\circ}) (because the central angle corresponding to arc (BC) is (2\times\angle BAC = 150^{\circ})), then (x=360 - 150=210^{\circ}).