Lines l and k are parallel to each other. A=120 degrees. and C=80 degrees. What is the number of degrees in B??
1 answer:
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°
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The problem can be solved step by step, if we know certain basic rules of summation. Following rules assume summation limits are identical.
Armed with the above rules, we can split up the summation into simple terms:
=> (a) f(x)=28n-n^2
=> f'(x)=28-2n
=> at f'(x)=0 => x=14
Since f''(x)=-2 <0 therefore f(14) is a maximum
(b) f(x) is a maximum when n=14
(c) the maximum value of f(x) is f(14)=196
Armed with the above rules, we can split up the summation into simple terms:
=> (a) f(x)=28n-n^2
=> f'(x)=28-2n
=> at f'(x)=0 => x=14
Since f''(x)=-2 <0 therefore f(14) is a maximum
(b) f(x) is a maximum when n=14
(c) the maximum value of f(x) is f(14)=196