MATHEMATICS HIGH SCHOOL

Find the measure of the exterior angle.

Answers

Answer 1

Answer:

Answer:

1) 128°

2) 126°

3) 108°

Question one:

The square in the corner means 90°. If you add the interior angles of any triangle together, you get 180. in this case, x is in exterior angle, so you subtract it from 180 to get the interior angle.

38 + 90 + (180-x) = 180

38 + 90 + 180 - x = 180

38 + 90 + 180 - 180 - x = 0

38 + 90 + 180 - 180 = x

128 = x

Question two:

again, adding all the interior angles makes 180°. use this to make the equation.

3x + (5x-6) + 90 = 180

3x + 5x - 6 = 90

8x = 96

x = 12.

x isn't the answer the question wants, however. if you look at the drawing, the angle that's supplementary to 5x-6 is the exterior angle. so,

180 - (5x-6) = the answer

180 - 5x + 6 = the answer

substitute x for 12

180 - 60 + 6 = the answer

126 = x

Question three

again, adding all the interior angles together makes 180°.

(a + 10) + 44 + (180-2a) = 180

a + 10 + 44 + 180 - 2a = 180

-a + 234 = 180

234 - 180 = a

54 = a

however, the question is looking for the exterior angle, not a. in this case, the exterior angle is 2a, so just multiply 54 by 2.

x = 108

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3. Determine whether or not AB is tangent to circle O. Show your work.

Answers

The line AB touching the circle at point B in the considered diagram is not tangent to the circle O.

What is Pythagoras Theorem?

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

$|AC|^2 = |AB|^2 + |BC|^2$

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

How are radius and tangent to a circle related?

There is a theorem in mathematics that:

If there is a circle O with tangent line L intersecting the circle at point A, then the radius OA is perpendicular to the line L.

So, if AB is a tangent, then ∠ABO = 90° and therefore satisfies Pythagoras theorem.

Assuming AB is tangent, then ABO is right angled we should get:

$H^2 = P^2 + B^2\n30^2 = 16^2 + 12^2\n900 = 256 + 144\n900= 500$

This statement is false, and therefore, so as our assumption is false that ABis tangent to circle O. Thus, AB is not tangent to circle O.

(so it might be that even if AB looks like touching at one point the circle O, but AB might be intersecting the circle at two points, or not touching it at all)

Thus, the line AB touching the circle at point B in the considered diagram is not tangent to the circle O.

Learn more about tangent to a circle here:

brainly.com/question/7942024

Answer:

not tangent

Step-by-step explanation:

two reasons, first

Triangle AOB is not a right triangle

line AB intersects the circle O at two points.

Find the product.

-a^2 b^2 c^2 (a + b - c)

Answers

−a^3b^2c^2−a^2b^3c^2+a^2b^2c^3

Which number is a common factor of 24, 48, and 144?16

10

9

8

Answers

8 is the common factor 24÷8=3 48÷8=6 144÷8=18

Give a real-world scenario in which you would write an inequality rather than an equation.

Answers

Example: You have some money in your pocket. You want to buy some snacks for tonight's match but your wife told you to buy one pizza on your way back to home that costs $10. That means that on snacks you can spend (y) :
y ≤ x - 10 where x represents money in your pocket.

This means that from money in your pocket you have to subtract $10 for pizza and out of remaining money you can spend some part of it on snacks or all of it.

List the values in decreasing order

Square root of 170, 13.5, 64/5, 13 7/8

Answers

thanks for the ponits

To begin an indirect proof you assume the converse of what you intend to prove is true

Answers

False. The converse may be either true or false, depending on what the original statement is, so assuming the converse would be pointless.

Answer:

false

Step-by-step explanation:

statement: if apple, than it is fruit

converse: if fruit, than it is apple (not always true)

The converse statement is sometimes true sometimes not