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Naddik [55]
3 years ago
13

Lines AB and CD (if present in the picture) are straight lines. Find x. Give reasons to justify your solutions.

Mathematics
1 answer:
Olin [163]3 years ago
8 0

Answer:

WORDS: The value of x is 15.

EQUATION: x = 15

Step-by-step explanation:

1. AB is a straight line therefore angles AOF, FOG, and GOB total 180º

2. If ∠FOG = 90º, AOF + GOB = 90º by subtraction & substitution property

3. 5x - 15 + 2x = 90 (now solve) --> by substitution

4. 7x - 15 = 90 --> by C.L.T. or <u>C</u>ombine <u>L</u>ike <u>T</u>erms

5. 7x = 105 --> by C.L.T. or <u>C</u>ombine <u>L</u>ike <u>T</u>erms

6. x = 15 --> by inverse operations (division)

Hope this helps!

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Complete the proof by providing the missing statement and reasons
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Answer:

In triangle SHD and triangle STD.

\overline{SD} \perp \overline{HT}          [Side]

Since, a line is said to be perpendicular to another line if the two lines intersect at a right angle.

⇒ \angle SDH = \angle SDT = 90^{\circ}

\overline{SH} \cong \overline{ST}       [leg]               [Given]

Reflexive property states that the value is equal to itself.

\overline{SD} \cong \overline{SD}       [Leg]       [Reflexive property]

HL(Hypotenuse-leg) theorem states that any two right triangles that have a congruent hypotenuse and a corresponding congruent leg are the congruent triangles.


then, by HL theorem;

\triangle SHD \cong \triangle STD                       Proved!



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ivanzaharov [21]
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If r = 5 units and x = 11 units, then what is the total surface area of the cylinder shown above?
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