A central angle and its intercepted arc have the same measure. True or False
1 answer:
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Answer:
B = 160°
Step-by-step explanation:
This is how I solved it (I hope the explanation isn't too confusing):
Since L and K are parallel, I drew a straight line from A to B. By doing this, I'm making a triangle: ΔABC
Then I solved for the angles of the triangle. First, we are given that ∠C = 80° and ∠A = 120°. Although, when I drew the vertical line from A to B, it made a 90° (see attachment).
So what we basically did was break ∠A into two parts: an angle inside ΔABC and one outside. To find the interior angle, simply subtract 90° from 120° to get 30°.
There are 180° in a triangle, so add the two interior angles you know:
30° + 80° = 110°
Then subtract 110° from 180° to find the final interior angle which is:
180° - 110° = 70°.
To find the measure of angle B, you must add all of the parts together, so the 90° outside angle and the 70° interior angle:
90° + 70° = 160°
