Question

Help me with my math quiz from friday 4/1 SHOW STEPS

Answer 1

Hie!! I will be solving the questions in the sequence of the attachments.

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4. As line SU and TV are intersecting each other at O.

A.T.Q, ∠UOV = (7x - 4)°

∠SOT = 87°

Then, ∠UOV = ∠SOT {Vertically Opposite Angles}

$\rightarrow\sf{7x - 4=87}$

$\rightarrow\sf{7x =87+4}$

$\rightarrow\sf{7x =91}$

$\rightarrow\sf{x =\frac{91}{7}}$

$\rightarrow\boxed{\bf{x =13}}$

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5. radius = 17ft

circumference of circle = 2πr

$\rightarrow\sf{circumference=2\times\frac{22}{7}\times17}$

$\rightarrow\boxed{\bf{circumference=106.8ft}}$

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3. ∠1 and ∠2 - add to 180 (linear pair)

∠1 and ∠3 - equal (Vertically Opposite Angles)

∠3 and ∠4 - add to 180 (linear pair)

∠2 and ∠4 - equal (Vertically Opposite Angles)

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2. 160° + (6x - 16)° = 180° (linear pair)

$\rightarrow\sf{6x - 16 = 180-160}$

$\rightarrow\sf{6x - 16 = 20}$

$\rightarrow\sf{6x = 20+16}$

$\rightarrow\sf{6x =36}$

$\rightarrow\sf{x =\frac{36}{6}}$

$\rightarrow\boxed{\bf{x =6}}$