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Answer:
See explanation
Step-by-step explanation:
If PK and PF are tangent to the circle, then the radii OK and OF are perpendicular to the lines PK and PF respectively.
Consider quadrilateral PFOK. The sum of the measures of all interior angles in quadrilateral PFOK is equal to 360°. Since OK and OF are perpendicular to the lines PK and PF, you have that
∠FOK+90°+∠KPF+90°=360°,
∠FOK=360°-90°-90°-∠KPF=180°-∠KPF.
Angles FOK and KOE are supplementary angles, then
∠KOE=180°-∠FOK=180°-(180°-∠KPF)=∠KPF.
Since angle KOE is central angle, the arc EK has the same measure as angle KOE and as angle KPF.
Answer:
x = 8
Step-by-step explanation:
Formula for sum of interior angles is 180(n - 2)
For a 5 sided polygon the sum is;
180(5 - 2) =540°
The supplement of ∡ 59° = 180° - 59° = 121°
The supplement of ∡ 77° = 180° - 77° = 103°
The supplement of ∡ 66° = 180° - 66° = 114°
The supplement of ∡ 62° = 180° - 62° = 118°
The sum of the polygon is:
121° + 103° + 114° + 118° + (180 - 12x)° = 540°
456° + (180 - 2x)° = 540°
(180 -12x)° = 540° - 456° = 84°
12x = 180° - 84° = 96°
x = 96/12 = 8
Answer:
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Step-by-step explanation:
