Question

Circle P is divided into four central angles by the diameters ⎯⎯⎯⎯⎯⎯⎯⎯ and ⎯⎯⎯⎯⎯⎯⎯⎯⎯ . The four central angles are ∠ , ∠ , ∠ , and ∠ .

The measure of ∠ is (+1)° and the measure of ∠ is (3–18)°.


Find the measure of ∠ to the nearest hundredth of a degree.

Answer 1

m<CPD =
`129.75^(o)`

Explanation:

From the given diagram,

m<APD ≅ m<BPC (vertically opposite angles)

m<APB ≅ m<CPD (vertically opposite angles)

But,

m<APD = (x + 1)

m<APB = (3x - 18)

In the given circle,

m<APD + m<BPC + m<APB + m<CPD = 360

(x + 1) + (x + 1) + (3x - 18) + (3x - 18) = 360

2(x + 1) + 2(3x - 18) = 360

2x + 2 + 6x - 36 = 360

8x - 34 = 360

8x = 360 + 34

8x = 394

x = 49.25

Thus,

m<CPD = (3x - 18)

= (3(49.255) - 18)

= 147.75 - 18

=
`129.75^(o)`

m<CPD =
`129.75^(o)`