Two horses approach each other along the same country road, one walking at 5.5 km/h and the other at 4.5 km/h. When the horses a
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Answer:
In the figure ∠ABO and ∠BCO have measures equal to 35°.
Step-by-step explanation:
<u><em>The complete question is</em></u>
For circle O, m CD=125° and m∠ABC = 55°
In the figure<____, (AOB, ABO, BOA) and <_____ (BCO, OBC,BOC) have measures equal to 35°
The picture in the attached figure
step 1
Find the measure of angle COB
we know that
----> by central angle
we have
therefore
step 2
we know that
AB is a tangent to the circle O at point A
so
ABC and ABO are right triangles
In the right triangle ABC
Find the measure of angle BCA
Remember that
---> by complementary angles in a right triangle
we have
substitute
step 3
In the triangle BCO
Find the measure of angle CBO
we know that
---> the sum of the interior angles in any triangle must be equal to 180 degrees
we have
-----> have measure equal to 35 degrees
substitute
step 4
Find the measure of angle ABO
In the right triangle ABO
we know that
----> by angle addition postulate
we have
substitute
----> have measure equal to 35 degrees
therefore
In the figure ∠ABO and ∠BCO have measures equal to 35°.
