Which statement is true about ∠JXM and ∠NXP? a.∠JXM and ∠NXP are complementary. b.∠JXM and ∠NXP are vertical. c.∠JXM and ∠NXP ar
e supplementary. d.∠JXM and ∠NXP are adjacent. I will give the brainiest
2 answers:
Answer:
Incomplete questions
Check attachment for correct question.
The correct answer is
A. ∠JXM and ∠NXP are complementary
step explanation:
line JP is a straight line and sum of angle on a straight line is 180°.
There are three angles on this straight line JP which are ∠JXM, ∠NXP and ∠MXN
Note: from the attachment, it is shown that ∠MXN is a right angle i.e. 90°.
Then, sum of angle on this line is 180°.
∠JXM + ∠NXP + ∠MXN = 180°
∠JXM + ∠NXP + 90° = 180°
∠JXM + ∠NXP = 180° — 90°
∠JXM + ∠NXP = 90°
From the definition of complementary angles : Two Angles are said to Complementary if their sum is 90° (a Right Angle).
They don't have to be next to each other, just so long as the sum is 90 degrees.
Then, since ∠JXM + ∠NXP add up to 90°, it shows that ∠JXM and ∠NXP are complementary
So the correct option is A
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Explanation:
There are two different formulas that are useful with the given information:
Area = (1/2)ab·sin(C)
Area = √(s(s-a)(s-b)(s-c)) . . . where s=(a+b+c)/2
It does not matter which sides are designated a, b, and c. Angle C will be opposite side c.
The third angle can be computed based on the fact that the sum of angles in a triangle is 180°. It will be 180° -32° -28° = 120°. The least-to-greatest order of the angles is the same as the least-to-greatest order of the length of the opposite side. So, we might have ...
- a = 7, A = 28°
- b = 8, B = 32°
- c = 13, C = 120°
Utilizing the first formula, the area is ...
Area = (1/2)(7)(8)sin(120°) = 14√3 ≈ 24.249 . . . square units
Utilizing the second formula, the area is ...
s = (7+8+13)/2 = 14
Area = √(14(14-7)(14-8)(14-13)) = 14√3 ≈ 24.249 . . . square units
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For the answer to be complete, it should be noted that using either of the other two angles will give different results for the area. That is because those angles are not exact values, but are rounded to the nearest degree. Using the first formula with the different angles, we get ...
- area = (1/2)(8)(13)sin(28°) ≈ 24.413 . . . square units
- area = (1/2)(7)(13)sin(32°) ≈ 24.111 . . . square units
The first of these answers is a little high because 28° is a little more than the actual value of the angle. Likewise, the second of these answers is a little low because 32° is slightly smaller than the actual angle.
In short, the most accurate information available should be used if the answer is to be the most accurate possible. If the angles are exact, then their values should be used. If the side measures are exact, then their values should be used. In general, it will be easier to make accurate measurements of the side lengths than to make accurate angle measurements.
