First, we are given that the inscribed angle of arc CB which is angle D is equal to 65°. This is half of the measure of the arc which is equal to the measure of the central angle, ∠O.
m∠O = 2 (65°) = 130°
Also, the measure of the angles where the tangent lines and the radii meet are equal to 90°. The sum of the measures of the angle of a quadrilateral ACOB is equal to 360°.
m∠O + m∠C + m∠B + m∠A = 360°
Substituting the known values,
130° + 90° + 90° + m∠A = 360°
The value of m∠A is equal to 50°.
<em>Answer: 50°</em>
<span>A) Goats that weigh exactly 50 or 60 pounds fall into two classes. would be the right answer</span>
Answer:
The measure of arc EBC is 220°
Step-by-step explanation:
step 1
Find out the measure of angle COB
we know that
m∠COB+m∠DOC=90° -----> given problem
we have that
m∠DOC=m arc DC -----> by central angle
m arc DC=50°
so
m∠DOC=50°
Find m∠COB
m∠COB+50°=90°
m∠COB=40°
step 2
Find out the measure of arc BC
we have that
m arc BC=m∠COB -----> by central angle
m∠COB=40°
therefore
m arc BC=40°
step 3
Find out the measure of arc EBC
we know that
m arc EBC=m arc EB+m arc BC
m arc EB=180° -----> because the diameter divide the circle into two equal parts
so
m arc EBC=180°+40°=220°
Step-by-step explanation:
