Lines cd and ce are tangent to circle a. if m∠dae = 130°, what is the measure of ∠dce?
230 degrees
130 degrees
100 degrees
50 degrees

The measure of ∠DCE is 50 degrees

Step-by-step explanation:

step 1

Find the measure of minor arc DE

we have

m∠DAE = 130°

we know that

m∠DAE=minor arc DE > by central angle

therefore

minor arc DE=130°

step 2

Find the measure of major arc DE

we know that

minor arc DE+major arc DE=360°

we have

minor arc DE=130°

substitute

130°+major arc DE=360°

major arc DE=360°-130°=230°

step 3

Find the measure of ∠DCE

we know that

The measurement of the outer angle is the semi-difference of the arcs which comprises

so

m∠DCE=(1/2)[major arc DE-minor arc DE]

substitute the values

m∠DCE=(1/2)[230°-130°]=50°

the degrees would remain the same ( the number to the left of the decimal point.

the multiply the decimal by 60 to get the minutes and use the numbers to the left of the decimal point.

then multiply the decimal portion of that by 60 for the seconds and round off as needed.

39 .956652

the 39 remains the degrees.

the minutes = 0.956652 x 60 = 57.39912

the minutes = 57

the seconds = 0.39912 x 60 = 23.95 = 24 ( rounded to nearest tenth)

so 39.956652 = 39 degrees, 57 minutes and 24 seconds

-75.159809

the -75 remains the degrees

the minutes = 0.159809 x 60 = 9.58854

the minutes = 9

the seconds = 0.58854 x 60 = 35.31, rounded to nearest tenth = 35.3 seconds

so -75.159809 = -75 degrees, 9 minutes and 35.3 seconds.

the first coordinate is north or south, since it it positive it is north.

the second number is east or west, because it is negative it is west.

39 degrees, 57 minutes and 24 seconds n

-75 degrees, 9 minutes and 35.3 seconds w

t= half of the arc subtended by t.

r= half of the arc subtended by r.  

t+r= half of the arc subtended by t + half of the arc subtended by r= half of 360=180

step-by-step explanation: