Answer:
<u> x = 16</u>
Step-by-step explanation:
See the attched figure
We should know that, one of the properties of the rhombus is the diagonals bisect the angles of the rhombus.
Given:
m∠ABC = 84 and m∠ABE = 3x − 6
So, m∠ABE = 0.5 * m∠ABC = 0.5 * 84 = 42
∴ 3x - 6 = 42
Solve for x
3x = 42 + 6 = 48
x = 48/3 = 16
<u>∴ x = 16</u>
Answer:
Step-by-step explanation:
Solving for x means you have to factor. First factor out the GCF of 2 to get:
and now we'll factor using the regular old method of ac and then factoring by grouping. In our polynomial, a = 3, b = 1, c = -6. Therefore, a times c is 3 * -6 which is -18. We need some combinations of the factors of 18 that will add to give us 1, the b term in the middle. The factors of 18 are:
1, 18
2, 9
3, 6 and that's it. Hm...it seems that won't work, so let's throw this into the quadratic formula, going back to the original and a = 6, b = 2 and c = -12:
and
and
and
and
which finally simplifies to
No wonder that didn't factor using the traditional method of factoring! We could have found that out by finding first the value of the discriminant, but oh well!