Find x, please. They’re vertical angles so x will be the same for both
1 answer:
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Answer: Probability that the next donation is not a pair of gloves is 0.54.
Step-by-step explanation:
Since we have given that
Number of coats = 5
Number of pairs of gloves = 23
Number of scarves = 19
Number of hats = 3
Total number of winter clothing is given by
Probability that the next donation is not a pair of gloves is given by
Not gloves = 50-23=27
P(not gloves ) is given by
Hence, Probability that the next donation is not a pair of gloves is 0.54.
<h3>Answer: A. 43</h3>
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Explanation:
Notice how inscribed angles x and y subtend (or cut off) the same minor arc measure. This means that x = y. So if we find x, we found y also.
The vertical line is a diameter of the circle. The blue angle marked in the diagram below is a right angle due to Thales Theorem, which is a special case of the inscribed angle theorem. Thales Theorem says that any inscribed angle in a semicircle is 90 degrees.
Therefore the triangle marked in red (same diagram) is a right triangle, allowing us to say
x+47+90 = 180
x+137 = 180
x = 180-137
x = 43
So y = 43 as well.
Answer:
3.) m < 7 = 155°, m < 8 = 25°
4.) m < 5 = 30°
m < 6 = 30°
m < 7 = 60°
m < 8 = 60°
Step-by-step explanation:
3.) By definition, angles that do not share a common side are called nonadjacent angles. Two nonadjacent angles formed by two intersecting lines are called vertical angles.
- Given that < PQT + < TQR = 180°
- Then it also means that the sum of <em>m</em> < 7 and <em>m</em> < 8 will also equal 180°.
- Also, < PQT ≅ < SQR because they are <u>vertical angles,</u> therefore, their measurements must also be congruent.
- Similarly, < PQS ≅ < TQR because they are <u>vertical angles</u>, and their measurements must also be congruent.
m < 7 = 5x + 5
m < 8 = x - 5
m < 7 + m < 8 = 180°
Substitute the values of m < 7 and m < 8 into the equation:
5x + 5 + x - 5 = 180°
6x + 0 = 180°
6x = 180°
Divide 6 on both sides of the equation to solve for x:
x = 30°
Plug in x = 30° to find the value of m< 7 and m< 8:
m < 7 = 5x + 5 = 5(30) + 5 = 150 + 5 = 155°
m < 8 = x - 5 = 30 - 5 = 25°
4.) This problem is an example of angles on a straight line. By definition, the sum of angles on a straight line is equal to 180°.
Therefore, the measurements of the following angles add up to 180°:
- < UVX + < XVY + < YVZ + <ZVW = 180°
- <em>m </em>< 5 + <em>m</em> < 6 + <em>m </em>< 7 + <em>m</em> < 8 = 180°
m < 5 = 5x
m < 6 = 4x + 6
m < 7 = 10x
m < 8 = 12x - 12
Substitute the values of each measurement onto the following equation:
5x + 4x + 6 + 10x + 12x - 12 = 180°
Combine like terms:
31x - 6 = 180°
Add 6 on both sides of the equation:
31x - 6 + 6 = 180° + 6
31x = 186
Solve for x:
x = 6
Plug in x = 6° to find the values of <em>m</em> < 5, <em>m</em> < 6, <em>m</em> < 7, and <em>m</em> < 8:
5(6) + 4(6) + 6 + 10(6) + 12(6) - 12 = 180°
180° = 180°
Therefore:
m < 5 = 5(6) = 30°
m < 6 = 4(6) + 6 = 30°
m < 7 = 10(6) = 60°
m < 8 = 12(6) - 12 = 60°