In triangle ABC, points N and M lie on sides AB and AC, respectively.Given AM = AN = BM = NC = BC, find m∠BAC.
1 answer:
Answer:
36°
Step-by-step explanation:
Please refer to the attached figure.
Triangles ANC, AMB, BCN, CBM are all isosceles by virtue of the given congruences. By symmetry, we also claim that ΔABC is isosceles (AB≅AC).
We aren't sure how their internal angles relate, but we can write a couple of equations.
Let x = m∠BAC, y = m∠BCN.
∠NCA = ∠NAC = ∠MBA = ∠MAB = x
∠BCM = ∠BMC = x +y
∠BMC = ∠MBA +∠MAB = 2x
So, we have ...
∠BMC = x +y = 2x ⇒ y = x
And the sum of angles around ΔABC is ...
x +(2x) +(2x) = 180°
x = 180°/5 = 36°
The measure of angle BAC is 36°.
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Complete Question
The mean finish time for a yearly amateur auto race was 186.94 minutes with a standard deviation of 0.305 minute. The winning car, driven by Roger, finished in 185.85 minutes. The previous year's race had a mean finishing time of 110.7 with a standard deviation of 0.115 minute. The winning car that year, driven by Karen, finished in 110.48 minutes.
Find their respective z-scores.
Who had the more convincing victory?
A. Roger had a more convincing victory because of a higher z-score.
B. Karen a more convincing victory because of a higher z-score.
C. Roger had a more convincing victory, because of a lower z-score.
D. Karen a more convincing victory because of a lower z-score.
Answer:
The correct option is D
Step-by-step explanation:
From the question we are told that
The mean of the current year is
The standard deviation is
The time taken by the winning car for the current year is
The mean of the previous year is
The standard deviation the previous year is
The time taken by the winning car for the previous year is
Generally the z-score for current year is mathematically evaluated as
=>
=>
Generally the z-score for previous year is mathematically evaluated as
=>
=>
From the value obtained we see that , Hence Karen had a more convincing victory because of the lower z -score.
Because we're given two points on the line, we can apply the slope formula to find the answer:
-4 - 8 / 2 - (-1)
-12 / 3
-4
<h3>The slope of the line is -4.</h3>