Mathematics, 28.02.2020 00:45 jfitness11

Circle D is shown. Line segments D E, D F, D G, and D H are radii. Angle E D F is 55 degrees, angle F D G is 70 degrees, and angle G D H is 110 degrees.
Which arc is congruent to Arc E H?

Arc G H
Arc F H
Arc G E
Arc F G

Answers: 3

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Answers

Answer from: Flameking1223

The figure is missing but we can solve the problem from the given information

Arc GE is congruent to arc EH ⇒ 3rd answer

Step-by-step explanation:

In a circle

The angle whose vertex is the center of the circle and its two sides are radii, is called central angleThe measure of the central angle is equal to the measure of its subtended arcThe measure of a circle is 360°

Look to the attached figure

In circle D

∵ D is the center of the circle

∵ DE and DF are radii

∴ ∠EDF is an central angle subtended by arc EF

- The measure of the central angle is equal to the measure

of its subtended arc

∴ m∠EDF = m of arc EF

∵ m∠EDF = 55°

∴ m of arc EF = 55°

∵ DF and DG are radii

∴ ∠FDG is an central angle subtended by arc FG

∴ m∠FDG = m of arc FG

∵ m∠FDG = 70°

∴ m of arc FG = 70°

∵ DG and DH are radii

∴ ∠GDH is an central angle subtended by arc GH

∴ m∠GDH = m of arc GH

∵ m∠GDH = 110°

∴ m of arc GH = 110°

∵ The measure of the circle = 360°

- The circle divided into 4 arcs EF, FG, GH and HE

∴ m arc EF + m arc FG + m arc GH + m arc HE = 360°

- Substitute the measures of arcs EF, FG and GH

∴ 55 + 70 + 110 + m arc HE = 360

∴ 235 + m arc HE = 360

- Subtract 235 from both sides

∴ m arc HE = 125°

∵ m of arc GE = m of arc EF + m of arc FG

∵ m of arc EF = 55°

∵ m of arc FG = 70°

∴ m of arc GE = 55 + 70 = 125°

∴ m of arc GE = m of arc EH

Arc GE is congruent to arc EH

Circle D is shown. Line segments D E, D F, D G, and D H are radii. Angle E D F is 55 degrees, angle

Answer from: Quest

answer: 80,000

step-by-step explanation:

the population doubles every day.

10,000*2=20,000 day 4

20,000*2=40,000 day 5

40,000*2=80,000 day 6

Answer from: Quest

hello,

b) 62.47% of the students are between 14 and 18 years old.

step-by-step explanation:

mean = 15 and standard deviation = 2

student between 14 to 18

formula used z-score

for age 14 , z score

using z-table , p(z> -0.5)=0.3085

for age 18 , z score

using z-table , p(z< 1.5)=0.9332

p(-0.5< z< 1.5)=0.9332-0.3085 = 0.6247

thus, 62.47% of the students are between 14 and 18 years old.

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Circle D is shown. Line segments D E, D F, D G, and D H are radii. Angle E D F is 55 degrees, angle...

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