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3 years ago

What is the value of x? Enter your answer in the box. X=

Mathematics

1 answer:

vodomira [7]3 years ago

7 0

Answer:

x = 80

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Sum the 3 angles and equate to 180

x + 30 + 70 = 180, that is

x + 100 = 180 ( subtract 100 from both sides )

x = 80

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Read 2 more answers

Find the approximate length of EF.

Yuri [45]

Answer:

The correct option is B

Step-by-step explanation:

Given information: ∠F=32°,∠D=54° and DF=18m.

According to the angle sum property of triangle, the sum interior angles of a triangle is 180°.

Using angle sum property, we get

$\angle D+\angle E+\angle F=180^{\circ}$

$54^{\circ}+\angle E+32^{\circ}=180^{\circ}$

$\angle E+86^{\circ}=180^{\circ}$

$\angle E=180^{\circ}-86^{\circ}$

$\angle E=94^{\circ}$

Law of sine:

$\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}$

Using law of sine we get

$\frac{\sin D}{d}=\frac{\sin E}{e}$

$\frac{\sin D}{EF}=\frac{\sin E}{DF}$

$\frac{\sin 54^{\circ}}{EF}=\frac{\sin 94^{\circ}}{18}$

$\frac{0.809016994375}{EF}=\frac{0.99756405026}{18}$

Cross multiply,

$0.809016994375\times 18=0.99756405026\times EF$

Divide both sides by 0.99756405026.

$EF=14.5978655656$

$EF\approx 14.6$

The value of EF is 14.6 m. Therefore the correct option is B.

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3 years ago