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°

30005

yes ok                                            

replace   with   27   and simplify.

10 , 27 , 10 , 70 , 10 , 35 , 10 , 48

step-by-step explanation: