2 intersecting lines are shown. A line with points M, H, K intersects a line with points L, H, J at point H. 4 angles are created. Clockwise, from the top, the angles are (5 m + 100) degrees, blank, blank, (2 m + 10) degrees.
What is the value of m?
10
30
70
150
To find the value of m, we need to use the fact that angles that are on a straight line add up to 180 degrees.
The top angle is given as (5m + 100) degrees.
The angle below it is a straight line angle, which means it is equal to 180 - (5m + 100) degrees.
The next angle is given as blank degrees.
The bottom angle is given as (2m + 10) degrees.
Since we have a total of 360 degrees in a circle, the sum of the angles in a quadrilateral is 360 degrees.
Therefore, we can write the equation:
(5m + 100) + (180 - (5m + 100)) + (blank) + (2m + 10) = 360.
Simplifying this equation, we get:
180 + (blank) + 2m + 10 = 360.
Combining like terms, we have:
(blank) + 2m + 190 = 360.
Subtracting 190 from both sides, we have:
(blank) + 2m = 170.
Now, we know that the sum of the two blank angles must be 180 degrees, since they are adjacent and form a straight angle.
Therefore, we can write the equation:
(blank) + (blank) = 180.
Substituting the value of (blank) from the previous equation, we have:
170 + (blank) = 180.
Subtracting 170 from both sides, we have:
(blank) = 10.
Therefore, the value of m is 10.
To find the value of m, we need to analyze the angles formed by the intersecting lines.
Clockwise, from the top, the angles are (5m + 100) degrees, unknown angle, unknown angle, (2m + 10) degrees.
Since the angles on a straight line add up to 180 degrees and the angles around a point add up to 360 degrees, we can set up an equation:
(5m + 100) + unknown angle + unknown angle + (2m + 10) = 360
Combining like terms, we get:
7m + 110 + unknown angle + unknown angle = 360
Now, let's solve for m:
7m + unknown angle + unknown angle = 250
Since the sum of the two unknown angles is equal to (180 - 100 - 10) = 70 degrees, we can substitute it back into the equation:
7m + 70 = 250
Subtracting 70 from both sides:
7m = 180
Dividing both sides by 7:
m = 180 / 7
Calculating the value of m:
m ≈ 25.714
Since none of the given options match "m ≈ 25.714", we can conclude that none of the provided answer choices is correct.