Question

NO LINKS. Find the measure of the angle or arc indicated. Part 2
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Answer 1

Solution given:

14.

34x+55x+2=180°[sum of opposite angle of a cyclic quadrilateral is supplementary]

89x=180°-2

x=178/89

x=2°

now

m arc VX=2× <H[ central angle is twice the inscribed angle standing on a same base]

m arc VX=2(34×2)=136°

Option C.

15.

Solution given:

<B=80°

<C=½ arc AB[central angle is twice the inscribed angle standing on a same base]

<C=½×120°=60°

we have

<A+<B+<C=180°[ sum of interior angle of a triangle is 180 ]

<A=180-80°-60°

<A=40°

option C.

Answer 2

9514 1404 393

Answer:

14. C) 136°

15. C) 40°

Explanation:

Inscribed angles are half the measure of the arc they intercept. For an inscribed quadrilateral, this means opposite angles are supplementary.

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14) ∠H +∠W = 180°

34x +55x +2 = 180

89x = 178 . . . . . . . . . subtract 2

x = 2 . . . . . . . . . . . . . divide by 89

arc VX = 2(34x) = 68(2) = 136 . . . degrees

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15) The sum of angles in the triangle is 180°.

? + 80° + (120°/2) = 180°

? = 40° . . . . . . . . . . subtract 140°