Quadrilaterals

what do you know about opposite angles in a parallelogram?

can you then set up a relation between (3x+17) and (5x-3) ?

can you use that relation to solve for x and thus angles ADC and ABC?

then can you use that to find the angle DAB ?
 
Romsek said:
what do you know about opposite angles in a parallelogram?

can you then set up a relation between (3x+17) and (5x-3) ?

can you use that relation to solve for x and thus angles ADC and ABC?

then can you use that to find the angle DAB ?
Click to expand...
The opposite sides of a parallelogram are of equal length and the opposite angles are of equal measure.
So, if I solve for x first I’ll find the missing angles of the parallelogram?
 
rachelmaddie said:
The opposite sides of a parallelogram are of equal length and the opposite angles are of equal measure.
So, if I solve for x first I’ll find the missing angles of the parallelogram?
Click to expand...

once you have x you have one pair of opposite angles.

you then have a pair of equal (as you noted) opposite angles that you are to solve for.

if you add up all these angles what must they sum to?

So figure out the value of the angles you don't know.
 
Romsek said:
once you have x you have one pair of opposite angles.

you then have a pair of equal (as you noted) opposite angles that you are to solve for.

if you add up all these angles what must they sum to?

So figure out the value of the angles you don't know.
Click to expand...
How do I set up the equation?
 
rachelmaddie said:
Combine like terms and numeric values?
Click to expand...

yer killin me smalls....

Have you not done algebra before? A pretty unfair problem to give you if not.

\(\displaystyle 3x+17=5x-3\\
20 = 2x\\
x = 10
\)

So each of those angles is \(\displaystyle 3(10)+17 = 47 = 5(10)-3\)

if we call the unknown angle \(\displaystyle y\) we then have

\(\displaystyle 2(47) + 2y = 360\)

can you finish from here?
 
Romsek said:
yer killin me smalls....

Have you not done algebra before? A pretty unfair problem to give you if not.

\(\displaystyle 3x+17=5x-3\\
20 = 2x\\
x = 10
\)

So each of those angles is \(\displaystyle 3(10)+17 = 47 = 5(10)-3\)

if we call the unknown angle \(\displaystyle y\) we then have

\(\displaystyle 2(47) + 2y = 360\)

can you finish from here?
Click to expand...
Solve for y?
 
there's only 2 facts you used here

a) opposite angles of a parallelogram are congruent
b) the interior angles of a quadrilateral sum to 2pi (360 deg)

all the rest is algebra
 
Romsek said:
there's only 2 facts you used here

a) opposite angles of a parallelogram are congruent
b) the interior angles of a quadrilateral sum to 2pi (360 deg)

all the rest is algebra
Click to expand...
The opposite sides of a parallelogram are of equal length and the opposite angles are of equal measure. The interior angles of a quadrilateral sum to 360 degrees.
Solve for x first to find one pair of opposite angles.
3x + 17 = 5x - 3
20 = 2x
x = 10
Substitute the value of x to solve for the angles.
3(10) + 17 = 47
5(10) - 3 = 47
Let the unknown value of the opposite angles be y.
Solve for y.
2(47) + 2y = 360
94 + 2y = 360
266 = 2y
y = 133
2(47) + 2(133) = 360
The measure of angle DAB is 133 degrees.
 
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