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

The measure of ∠DCE = 50°

Step-by-step explanation:

Given:

m∠ DAE = m∠ A = 130°

As lines CD and DE are tangent to circle at the point of contact D and E.

So for a tangent at point of contact the measure angle is 90°

∴ m∠ D =  m∠ E = 90°

To Find:

m∠ C = ∠ DCE = ?

Solution:

As lines CD and DE are tangent to circle at the point of contact D and E.

So for a tangent at point of contact the measure angle is 90°

∴ m∠ D =  m∠ E = 90°

AECD is a quadrilateral.

m∠ A + m∠ E + m∠ C + m∠ D =360° {Sum of angles of Quadrilateral is 360°}

substituting the given values we get

130 + 90 + m∠ DCE + 90 = 360°

∴ m∠ DCE + 310 = 360°

∴ m∠ DCE = 360 - 310

∴ m∠ DCE = 50°

Therefore the measure of ∠ DCE is 50°

3

step-by-step explanation:

in standard form:

a= dictionaries

b= maps

you have to buy 3 dictionaries, so put a 3 next to the a (dictionaries) so that you can multiply them by each other.

a3+b= 60 (the amount of money you have)

we already know the cost of a=15 so replace a with $15

($15 x 3)+b=60

multiply 15 and 3 to get $45 and replace it with $45

45+b=60

and then replace b with 15 to get the total:

45+15=60

that means you have $15 left after buying 3 dictionaries.

15 divided by the cost of a map ($5) equals 3.

so you can buy 3 maps.

sorry if it was confusing!

coins of silver or gold

step-by-step explanation: