Carlos and Maria played a game of rolling two number cubes and finding the sum of the numbers. They recorded how many times each sum was
rolled in the table below.

sum frequency
2 16
3 1
4 5
5 7
6 8
7 18
8 20
9 14
10 14
11 5
12 5

Which statement is true?
A. A sum of 8 was rolled about 14% of the time.
B. A sum of 2 was rolled about 1.8% of the time.
C. A sum of 9 or 10 was rolled about 25% of the time.
D. A sum of 5 or 6 was rolled about 10.1% of the time.

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°

graph b

step-by-step explanation:

one solution- graph a (clear intercepting point.)

no solution- graph b (they're parallel, there will never be a point of interception.)

infinite solutions- graph c (all points intercept.)

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