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solve questions 14-15

45 points solve questions 14-15-example-1
User Opsidao
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2 Answers

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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.

User Tom Burrows
by
8.4k points
5 votes

Answer:

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°

User APH
by
7.6k points

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