Answer:
∠NMC = 50°
Step-by-step explanation:
The interpretation of the information given in the question can be seen in the attached images below.
In ΔABC;
∠ A + ∠ B + ∠ C = 180° (sum of angles in a triangle)
∠ A + 70° + 50° = 180°
∠ A = 180° - 70° - 50°
∠ A = 180° - 120°
∠ A = 60°
In ΔAMN ; the base angle are equal , let the base angles be x and y
So; x = y (base angle of an equilateral triangle)
Then;
x + x + 60° = 180°
2x + 60° = 180°
2x = 180° - 60°
2x = 120°
x = 120°/2
x = 60°
∴ x = 60° , y = 60°
In ΔBQC
∠a + ∠e + ∠b = 180°
50° + ∠e + 40° = 180°
∠e = 180° - 50° - 40°
∠e = 180° - 90°
∠e = 90°
At point Q , ∠e = ∠f = ∠g = ∠h = 90° (angles at a point)
∠i = 50° - 40° = 10°
In ΔNQC
∠f + ∠i + ∠j = 180°
90° + 10° + ∠j = 180°
∠j = 180° - 90°-10°
∠j = 180° - 100°
∠j = 80°
From line AC , at point N , ∠y + ∠c + ∠j = 180° (sum of angles on a straight line)
60° + ∠c + ∠80° = 180°
∠c = 180° - 60°-80°
∠c = 180° - 140°
∠c = 40°
Recall that :
At point Q , ∠e = ∠f = ∠g = ∠h = 90° (angles at a point)
Then In Δ NMC ;
∠d + ∠h + ∠c = 180° (sum of angles in a triangle)
∠d + 90° + 40° = 180°
∠d = 180° - 90° -40°
∠d = 180° - 130°
∠d = 50°
Therefore, ∠NMC = ∠d = 50°
I think you can only say that the width of the quadrilateral will be 5.
OH no it will be a rectangle and the length will be 1/2 * 20 = 10
so the perimeter is 2*5 + 2*10 = 30 <---- answer
Answer:B 55
Step-by-step explanation:
Answer:
There are 42 quarters (and 6 dimes).
Step-by-step explanation:
The given ratio is 2:14. But this does not tell us how many dimes nor how many quarters we have. Instead, it's a ratio. Modify this by multiplying numerator and denominator by n and then find n:
Number of dimes 2n
----------------------------- = -----
Number of quarters 14n
Then the total number of coins is 2n + 14n =48, implying that:
16n = 48, or n = 3.
Then the number of dimes is 2(n) = 2(3) = 6, and that of quarters is 14(n) =
14(3) = 42.
There are 42 quarters (and 6 dimes). Notice how the total of 42 and 6 is 48.