Question

45 points
solve questions 14-15

Answer 1

14. DF is 82°.

15. ∠PQR is 59°.

14. secant-secant angle CEG is equal to half the difference between the intercepted arcs' measurements, that is

∠ CEG = (DF - CG)

To eliminate the fraction, multiply both sides by 2 and apply 44° = ( 170 - DF).

88° = 170 - DF (Deduct 170 from each side.)

Multiply both sides by - 1 to get - 82 = - DF, and then

DF is 82°.

15. Half of the difference in the intercepted arcs' measurements is the tangent-tangent angle PQR.

The PSR and RP arcs were intercepted.

Since a circle's arcs add up to 360°,

360° - RP = 360° - 121° = 239° is PSR.

then

( 239 - 121)° = × 118° = 59° is the ∠PQR.

Answer 2

b and d

Explanation:

14

the secant- secant angle CEG is half the difference of the measures of the intercepted arcs, that is

∠ CEG =
`(1)/(2)` (CG - DF)

44° =
`(1)/(2)`( 170 - DF) ← multiply both sides by 2 to clear the fraction

88° = 170 - DF ( subtract 170 from both sides )

- 82 = - DF ( multiply both sides by - 1 ) , then

DF = 82°

15

the tangent- tangent angle PQR is half the difference of the measures of the intercepted arcs.

the intercepted arcs are PSR and RP

the sum of the arcs in a circle = 360° , so

PSR = 360° - RP = 360° - 121° = 239°

then

∠ PQR =
`(1)/(2)` ( 239 - 121)° =
`(1)/(2)` × 118° = 59°