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Nata [24]
2 years ago
8

Find the value of x in each case.

Mathematics
1 answer:
AnnZ [28]2 years ago
6 0

Answer:

x = 23

Step-by-step explanation:

<u>Alternate Interior Angles Theorem</u>

If a line intersects a set of parallel lines in the same plane at two distinct points, the alternate interior angles that are formed are <u>congruent</u>.

Therefore, as line EF is parallel to line AC (indicated by the arrows), and EB intersects them:

⇒ ∠ABE = ∠FEB

⇒ ∠ABE = 4x

<u>Angles on a straight line sum to 180°</u>

⇒ ∠FBE + ∠ABE + ∠ABD = 180°

⇒ 65 + 4x + x = 180

⇒ 65 + 5x = 180

⇒ 65 + 5x - 65 = 180 - 65

⇒ 5x = 115

⇒ 5x ÷ 5 = 115 ÷ 5

⇒ x = 23

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(Since the perimeter is the length of each sides added up. Two sides are equal to x+6 and two are equal to x-6)

2 (x+6) + 2 (x-6) = 48

(break out the brackets)

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( 12 and -12 cancel out and "disappear".)

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Feel free to ask if you have any questions

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Step-by-step explanation: Good luck...

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In ΔJKL, the measure of ∠L=90°, JK = 7.3 feet, and KL = 4.7 feet. Find the measure of ∠J to the nearest tenth of a degree.
Yakvenalex [24]

Answer:

40°

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We can find the  tangent of ∠J using the trigonometrical ratios which may be expressed in the form SOA CAH TOA Where,

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Considering triangle ΔJKL, where ∠L=90°, JK = 7.3 feet, and KL = 4.7 feet

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