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MrMuchimi
2 years ago
14

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

Mathematics
2 answers:
sergeinik [125]2 years ago
6 0

9514 1404 393

Answer:

  14.  C) 136°

  15.  C) 40°

Step-by-step explanation:

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

__

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

__

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

  ? + 80° + (120°/2) = 180°

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

Reil [10]2 years ago
5 0

Answer:

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°

<u>now</u>

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

m arc VX=2(34×2)=<u>1</u><u>3</u><u>6</u><u>°</u>

<u>Option</u><u> </u><u>C</u><u>.</u>

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=<u>4</u><u>0</u><u>°</u>

<u>o</u><u>p</u><u>t</u><u>i</u><u>o</u><u>n</u><u> </u><u>C</u><u>.</u>

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