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3 years ago

Find the measure of each angle. Assume the lines are parallel, I dont have a protractor small enough to do this job.

Mathematics

1 answer:

Sholpan [36]3 years ago

4 0

Answer:

All angles are 113 or 67. See below for each angle measure.

Step-by-step explanation:

Parallel lines cut by a transversal have several angle relationships which can be used to find an unknown angle measure:

• Alternate Interior Angles are angles across the transversal between pairs of parallel lines. These angles are congruent. Example: 8 and 4 are congruent and are pairs of alternate interior angles. 7 and 3 are another set.

• Alternate Exterior Angles are angles across the transversal outside of the parallel lines. These angles are congruent. Example 1 & 5 are congruent alternate exterior angles. 2 and 6 are another set.

• Supplementary angles are angles which form a line and add to 180. If angle 1 + angle 2 = 180 and angle 1 = 113, then 113 + Angle 2 =180. Angle 2 must be 67 degrees.

• Vertical angles are angles across a vertex. They are congruent. Example: Angle 2 and Angle 8 are both 67.

Using these relationships, the following angles have the following measures:

Angle 1 = 113

Angle 2 = 67

Angle 3 = 113

Angle 4 = 567

Angle 5 =113

Angle 6 = 67

Angle 7 = 113

Angle 8 = 67

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vichka [17]

Answer:

y = -3(x - 4)² - 2

Step-by-step explanation:

Given the vertex, (4, -2), and the point (2, -14):

We can use the vertex form of the quadratic equation:

y = a(x - h)² + k

Where:

(h, k) = vertex

a = determines whether the graph opens up or down, and it also makes the parent function wider or narrower.

positive value of a = opens upward
negative value of a = opens downward
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a > 1, the graph is narrower than the parent function.

h = determines how far left or right the parent function is translated.

h = positive, the function is translated h units to the right.
h = negative, the function is translated |h| units to the left.

k determines how far up or down the parent function is translated.

k = positive: translate k units up.
k = negative, translate k units down.

Now that I've set up the definitions for each variable of the vertex form, we can determine the quadratic equation using the given vertex and the point:

vertex (h, k): (4, -2)

point (x, y): (2, -14)

Substitute these values into the vertex form to solve for a:

y = a(x - h)² + k

-14 = a(2 - 4)² -2

-14 = a (-2)² -2

-14 = a4 + -2

Add to to both sides:

-14 + 2 = a4 + -2 + 2

-12 = 4a

Divide both sides by 4 to solve for a:

-12/4 = 4a/4

-3 = a

Therefore, the quadratic equation inI vertex form is:

y = -3(x - 4)² - 2

The parabola is downward-facing, and is vertically compressed by a factor of -3. The graph is also horizontally translated 4 units to the right, and vertically translated 2 units down.

Attached is a screenshot of the graph where it shows the vertex and the given point, using the vertex form that I came up with.

Please mark my answers as the Brainliest, if you find this helpful :)

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Answer:

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Step-by-step explanation:

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