In quadrilateral STAR, one pair of opposite sides and one pair of opposite angles are _____ and _____.
ST and TA, angle S and angle A
ST and RA, angle S and angle T
TA and AR, angle T and angle R
TA and SR, angle A and angle S
In parallelogram PQRS, find the value of angle SPR if angle RSP is 75° and angle PRS is 39°.
In parallelogram ABCD, angle A is 3x + 12 and angle B is 132°. Show your work in finding the value of x.
ST and TA, angle S and angle A
ST and RA, angle S and angle T
TA and AR, angle T and angle R
TA and SR, angle A and angle S
In parallelogram PQRS, find the value of angle SPR if angle RSP is 75° and angle PRS is 39°.
In parallelogram ABCD, angle A is 3x + 12 and angle B is 132°. Show your work in finding the value of x.
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If the letters S T A and R mark off consecutive angles in that order (whether clockwise or anticlockwise), then opposite sides cannot share a letter (ST and TA cannot be opposite sides because they meet at the corner called T)..Opposive angles cannot be consecutive letters (S cannot be opposite T, S cannot be opposite R - you have to consider the sequence of angles as if they formed a cycle, so S follows R).
In a parallelogram, since opposite sides are parallel (hence the name), two adjacent angles must add up to 180. One way to convince your self: consider that you are coming down one side, you turn to follow the bottom side, then turn again to go up the other side. In these two turns, you yave turned completely around (180 degrees).
A diagonal (PR for example) cuts the parallelogram into two triangles. The angles given belong to the triangle PRS, and they add up to 114. Since the sum of inner angles in ANY flat triangle is 180, then angle S (angle RSP if you prefer) must be 180 - 114. This means that the full angle R (angle QRS) must be 180 - S = 180 - (180 - 114)) = 114.
Angle P, which is opposite R is also an angle adjacent to angle S, must also be 180 - (180 - S), which makes it equal to R.
If you continue the reasoning, you will find that angle Q (opposite S) must be the same as S.
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If A and B are two consecutive angles in a parallelogram, then they must add up to 180 (we saw why earlier).
180 = (3x + 12) + 132
solve for x
In a parallelogram, since opposite sides are parallel (hence the name), two adjacent angles must add up to 180. One way to convince your self: consider that you are coming down one side, you turn to follow the bottom side, then turn again to go up the other side. In these two turns, you yave turned completely around (180 degrees).
A diagonal (PR for example) cuts the parallelogram into two triangles. The angles given belong to the triangle PRS, and they add up to 114. Since the sum of inner angles in ANY flat triangle is 180, then angle S (angle RSP if you prefer) must be 180 - 114. This means that the full angle R (angle QRS) must be 180 - S = 180 - (180 - 114)) = 114.
Angle P, which is opposite R is also an angle adjacent to angle S, must also be 180 - (180 - S), which makes it equal to R.
If you continue the reasoning, you will find that angle Q (opposite S) must be the same as S.
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If A and B are two consecutive angles in a parallelogram, then they must add up to 180 (we saw why earlier).
180 = (3x + 12) + 132
solve for x
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TA and SR, angle A and angle S
is your first answer because sides and angles can't repeat..
180 - 75 - 39 = 66
66 is your second answer
for the third, set it up like
3x + 12 + 132 = 180
3x + 144 = 180
3x = 36
x = 12
EDIT (I'll help with the other one as well)
first you set them up to equal each other
4x+1 = 2x+7
Then you get them on the correct sides
2x = 6
x = 3
Plug it back in for the angles measure which will be
4(3) + 1 = 13
13 is the angle
is your first answer because sides and angles can't repeat..
180 - 75 - 39 = 66
66 is your second answer
for the third, set it up like
3x + 12 + 132 = 180
3x + 144 = 180
3x = 36
x = 12
EDIT (I'll help with the other one as well)
first you set them up to equal each other
4x+1 = 2x+7
Then you get them on the correct sides
2x = 6
x = 3
Plug it back in for the angles measure which will be
4(3) + 1 = 13
13 is the angle