Focus on the top line angles for now.
Those two angles combine to the straight angle ABC, which is 180 degrees.
(angleABY) + (angleYBC) = angle ABC
(x+25)+(2x+50) = 180
(x+2x) + (25+50) = 180
3x+75 = 180
3x = 180-75
3x = 105
x = 105/3
x = 35
We'll use this x value to find that:
- angle YBC = 2x+50 = 2*35+50 = 70+50 = 120 degrees
- angle BEF = 5x-55 = 5*35-55 = 175-55 = 120 degrees
Angles YBC and BEF are corresponding angles (they are both in the northeast corner of their respective four-corner angle configuration). They are both 120 degrees. Since we have congruent corresponding angles, we have effectively proven that AC is parallel to DF. Refer to the converse of the corresponding angles theorem.
The regular version of the "corresponding angles theorem" says that if two lines are parallel, then the corresponding angles are congruent. The converse reverses the logic of the conditional statement. Meaning that if the corresponding angles are congruent, then the lines are parallel.
Answer:
The modes are 9 and 11
Step-by-step explanation:
To find the factor a a polynomial from its roots, we are going to seat each one of the roots equal to
, and then we are going to factor backwards.
We know for our problem that one of the roots of our polynomial is -3, so lets set -3 equal to
and factor backwards:
is a factor of our polynomial.
We also know that another root of our polynomial is
, so lets set
equal to
and factor backwards:
(
is a factor of our polynomial.
We can conclude that there is no correct answer in your given choices.
Answer:A
Step-by-step explanation:
Answer:
The solution and complete explanation for the above question and mentioned conditions is given below in the attached document.i hope my explanation will help you in understanding this particular subject.
Step-by-step explanation: