In quadrilateral EFGH, EF is parallel to HG, measure of angle E = y+10, measure of angle F = 2y-40, and measure of angle H = 2y-31. Measure of angle G is?
2006-11-28 19:02:31 · 6 answers · asked by DookieCookie 4 in Science & Mathematics ➔ Mathematics
total angle of quadrilateral EFGH is 360
so, the measure of angle G is
= 360 - (y + 10) - (2y - 40) - (2y - 31)
= 421- 5y
2006-11-28 19:11:20 · answer #1 · answered by csp 2 · 0⤊ 0⤋
I would like to state out something clear before I answer this question. A quadrilateral is not neccessary a parallelogram. The question did not state that FG is parallel to EH. As the question said that EF is parallel to HG, this quadrilateral is actually a trapezium. Therefore, F + H is not neccessary equals to 180, so is G + E = 180.
In a quadrilateral or a trapezium, the total degree is 360.
Therefore, the measure of angle G is calculated as following:
360 - (2y - 40) - (y + 10) - (2y - 31)
= 360 - 2y + 40 - y -10 -2y + 31
= 421 - 5y
The answer only asks for the measure of angle G, and not the value of y. However, as the information given is not sufficient, the value of y could not be find. The answer could only be stated in terms of y.
2006-11-29 03:44:04 · answer #2 · answered by Anonymous · 1⤊ 0⤋
y+1
2006-11-29 03:50:26 · answer #3 · answered by wr.05 1 · 0⤊ 1⤋
Being EF parallel to HG,
Angle
F+H = 180
so, 2y-40 + 2y-31 = 180
y = (180+71)/4 = 62.75
So angle E = y + 10 = 72.75
Being EF parallel to HG,
Angle E + G = 180
so, 72.75 + G = 180
Thus, G = 180-72.75 = 107.25
Answer, G = 107.25
2006-11-29 03:15:03 · answer #4 · answered by M1976 2 · 0⤊ 0⤋
If E+F=H+G=180 degrees
(y+10)+(2y-40)=G+(2y-31)
3y-30=G+2y-31
G=y+1
G+H=180
y+1+2y-31=180
3y=210
y=70
G=71 degrees
2006-11-29 03:22:24 · answer #5 · answered by ? 1 · 0⤊ 0⤋
assuming that G = y
360 = Y + Y+10 + 2Y-40 + 2Y - 31
360 = 6Y -61
421 = 6Y
Y = 70.16666666666666666666666666666666666666666666666
But I am not sure
2006-11-29 03:12:02 · answer #6 · answered by tomkat1528 5 · 0⤊ 1⤋