Find Arc Measures of two diameters
1 answer:
Answer:
m arc ACD =310
m arc AC = 130
Step-by-step explanation:
drawing the figure helps
if you do, should get something like the figure below
filling in arc ad as 50 degrees tells you that the angle describing it is also 50 degrees; it's a central angle.
and we know that 1/2 of a circle is 180 degrees. so if you subtract 50 from 180 you'll get 130 which will be your measurement for arc AC (because it is a central angle and AC
+AD completes the 180 half.).
as well as that to get ACD, well 1st we know that arc AC is within arc ACD. that would mean that ACD has to be more than 130.
what you can do is subtract 50 from 360. the entire circle is 360, but seeing as the arc is ACD (The rest of the circle excluding arc AD since we aren't looking for that measurement) we can just subtract.
subtracting 50 from 360 will give you 310
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Answer:
x is approximately 69.39 degrees.
Step-by-step explanation:
To find x in this triangle, we can use the sin rule:
The corresponding angle for each length is the one that lies directly opposite it. E.g. if 3.5 was our length 'a', then 55 degrees would be our angle A.
So let's take 3.5 and 55degrees as our length and Angle A, and 4 and x degrees as our length and angle B as we are trying to solve for x.
This would give us the following equation:
Since we are solving for an angle, it will be easier to rearrange the equation if we have it as the numerator, so we can flip the fractions to make it easier. It will still be equal as we are looking for the ratio.
From here let's isolate the sin(x) by multiplying by 4 and solving the values we have so far:
Now the final step is to use inverse sin to cancel the sin so we just have x:
x is approximately 69.39 degrees.
Hope this helped!