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Answer:
m∠A = 72°.
m<B = 108°.
Step-by-step explanation:
In a parallelogram, the opposite angles are congruent.
Therefore, we can set the two expressions equal to each other:
5y - 3 = 3y + 27
Add 3 to both sides:
5y = 3y + 30
Subtract 3y from both sides:
2y = 30
Divide both sides by 2:
y = 15
Substitute this value of y into an expression to solve for the measure of ∠A:
5(15) - 3 = 72°. m∠A = 72°.
In parallelograms, the neighboring angles are supplementary. Therefore:
m∠A + m∠B = 180°
72° + m∠B = 180°
m<B = 108°.
Answer:
904cm3 just use an online sphere calculator they're easy to use
Answer:
The length is 23 inches and the width is 6 inches.
Step-by-step explanation:
The perimeter for a rectangular shape is represented as:
P = 2L + 2W, where L represents length and W represents width
We can represent the length as:
L = 3W + 5
Substituting this into the perimeter function, we get:
P = 2 (3W + 5) + 2W
Substituting 58 for P, we get:
58 = 2 (3W + 5) + 2W
58 = 6W + 10 + 2W
58 = 8W + 10
58 - 10 = 8W + 10 - 10
48 = 8W
48 / 8 = 8W / 8
6 = W
With 6 being the established value for the width, we can substitute this back into the equation for length:
L = 3W + 5
L = 3(6) + 5
L = 18 + 5
L = 23
To check our work, we can substitute both the width and length into the perimeter equation:
P = 2L + 2W
58 = 2(23) + 2(6)
58 = 46 + 12
58 = 58
Therefore, length is 23 inches and the width is 6 inches.
