1. In the figure below ABC∡=153°, ABD∢=(5x+5)°, and DBC∢=(3x+12)°. Find the measure of ABD∢ and DBC∢. Show all work
1 answer:
By angle addition postulate,
m(∠ABD) + m(∠DBC) = m(∠ABC)
Now substitute the values of each angle,
(5x + 5)° + (3x + 12)° = 153°
Combine like terms of the expression,
(5x + 3x) + (5 + 12) = 153
8x + 17 = 153
8x = 153 - 17
x =
x = 17
Substitute the value of 'x' to get the measure of each angle,
m(∠ABD) = (5x + 5)
= 5(17) + 5
= 90°
m(∠DBC) = (3x + 12)
= 3(17) + 12
= 63°
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Dustin has a bag of marbles with 4 blue marbles, 4 white marbles, and 3 red marbles. There are 11 marbles in total.
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the probability that the second marble drawn is red marble is
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B. The probability that the first marble drawn is red marble is
the probability that the second marble drawn is white marble is
The probability that the first marble drawn is red and the second is white is
C. The probability that the first marble drawn is blue marble is
the probability that the second marble drawn is blue marble is
the probability that the third marble drawn is blue marble is
The probability that the first, second and third marbles drawn are blue is