Given that QRST is a parallelogram, find the angle measures:

Mathematics

2 answers:

Mamont248 [21]3 years ago

4 0

Answer:

below

Step-by-step explanation:

consecutive angles are supplementary in parallelogram

q+t = 180

3x+5+9x-17 = 180

12x-12 = 180

x-1 = 15

x=16

r=t = 127°

q=s = 53°

kumpel [21]3 years ago

3 0

Answer:

Angle R is 127 degrees and Angle S is 53 degrees

Step-by-step explanation:

We know that adjacent angles in a parallelogram are supplementary, meaning that they add up to 180 degrees.

With this, we can create an equation to solve for x with the values given for Q and T

Q+T = 180

(3x+5)+(9x-17) = 180

12x -12 = 180

12x = 192

x = 16

Now we can find the angles of Q and T given the value of x

Q = (3x+5)

Q = (3*16+5)

Q = 53 degrees

T = (9x-17)

T = (9*16-17)

T = 127 degrees

Since opposite angles in a parallelogram are congruent,

angle S = angle Q and angle R = angle T

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Alona [7]

Answer:

<h3>b) A cylinder in which h = 3 and d = 6 has a volume of 27π in^3; therefore, Wilson is correct.</h3>

Step-by-step explanation:

$\text{The formula of a volume of a cone:}\\\\V_{cone}=\dfrac{1}{3}\pi r^2H\\\\r-radius\\H-height\\\\\text{The formula of a volume of a cylinder:}\\\\V_{cylinder}=\pi r^2H}\\\\\text{If the cylinder and the cone have the same diameter,}\\\text{then have the same radius.}\\\\diameter\ d=2r\to r=\dfrac{d}{2}\\\\d=6\ in\to r=\dfrac{6}{2}=3\ in\\\\\text{Substitute:}\\\\V_{cone}=9\pi\ in^3,\ r=3\ in:\\\\9\pi=\dfrac{1}{3}\pi(3^2)(H)\\\\9\pi=3H\pi\qquad\text{divide both sides by}\ 3\pi\\\\3=H\to H=3\ in$