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2 years ago

NOTE: Angles not necessarily drawn to scale.

Mathematics

1 answer:

jeka57 [31]2 years ago

6 0

Answer:

x = 45°

Step-by-step explanation:

Vertical Angle Theorem

When two straight lines intersect, they form two pairs of angles. The vertically opposite (non-adjacent) angles are congruent (equal).

From inspection of the given diagram, the straight line with points C and D and the straight line with points F and G intersect at point E.

Therefore, angles ∠FEC and ∠DEG are vertically opposite, and so they are equal.

From inspection of the diagram:

∠FEC = x°
∠DEG = 20° + 25° = 45°

Therefore:

⇒ ∠FEC =∠DEG

⇒ x = 45°

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lbvjy [14]

Given:

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Line w passes through point (-6,10) and it is parallel to the line v.

To find:

The equation in slope intercept form of line w.

Solution:

Slope intercept form of a line is

$y=mx+b$ ...(i)

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We have,

$y=\dfrac{3}{4}x-11$ ...(ii)

On comparing (i) and (ii), we get

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$m_2=-\dfrac{4}{3}$

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Line v is parallel to line w. So, slope of line v is also $-\dfrac{4}{3}$ .

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$y-10=-\dfrac{4}{3}(x+6)$

$y-10=-\dfrac{4}{3}x-\dfrac{4}{3}(6)$

$y-10=-\dfrac{4}{3}x-8$

Adding 10 on both sides, we get

$y=-\dfrac{4}{3}x-8+10$

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Anettt [7]

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