Angle x + 16 and Angle 4x - 5. They are vertical angles. Solve for x and the measure of the two angles.

Mathematics

1 answer:

inna [77]4 years ago

4 0

Answer:

Vertical angles are congruent and have equal measures. Therefore,

Simplify and solve for x :

x + 16 = 4x -5.

16=3x-5

21=3x

x=7

Thus the angles measure is x+16 = 7+16 = 23 degrees, for both angles (for each of the two vertical angles).

Step-by-step explanation:

each angle measure is 23 degrees

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blagie [28]

Answer:

19.41 units

Step-by-step explanation:

Given coordinates of points;

(-10, 9)
(-6, -10)

To determine the distance between the two points, the distance formula is required. The distance formula is used where it is not possible to calculate the distance through a straight line. The distance formula is expressed as,

⇒ $\sqrt{(x_{2} - x_{1})^{2} + (y_2 - y_1)^{2} }$

The distance between the two points can be determined by plugging the coordinates into the formula;

⇒ $\sqrt{(x_{2} - x_{1})^{2} + (y_2 - y_1)^{2} }$
⇒ $\sqrt{[-6 - (-10)]^{2} + [-10 - 9]^{2} }$

Then, we can simplify the root as needed to determine the distance;

⇒ $\sqrt{[-6 + 10]^{2} + [-19]^{2} }$
⇒ $\sqrt{[4]^{2} +361 }$
⇒ $\sqrt{16 +361 }$
⇒ $\sqrt{377}$

Finally, we need to convert the root into decimals (stated in question). It is impossible to determine the root in decimal form. Therefore, I used a calculator to determine the distance in decimal form.