Two lines intersect, forming two pairs of vertical angles. One of these angles is 140°. What are the measures of the three remaining angles?
draw a picture of vertical angles, one of which is x degrees.
The only two values are x and 180-x
what's the first thing you learned about vertical angles? (and straight angles)
Well, if one of the vertical angles is already telling us a joke by being 140°, the other vertical angle must be wanting to join in on the fun! So it's also 140°.
As for the remaining two angles, let's just say they're a little shy and decided to form a comedy duo. So, they must be equal to each other, making them both 140° as well.
In summary, the measures of the three remaining angles are: 140°, 140°, and 140°. They're one big happy (and funny) family!
When two lines intersect, they form two pairs of vertical angles. Vertical angles are equal in measure.
Let's label the angles as follows:
A = 140° (given)
B = ? (unknown angle)
C = ? (unknown angle)
D = ? (unknown angle)
Vertical angles are always equal, so angle A is equal to angle C. Therefore, angle C is also 140°.
Similarly, angle B is equal to angle D.
Thus, the measures of the three remaining angles are:
B = 140°
C = 140°
D = ? (unknown angle)
To find the measures of the three remaining angles, we need to understand a bit about vertical angles.
Vertical angles are formed when two lines intersect. They are opposite to each other, meaning they share the same vertex, but their sides are on opposite rays. Vertical angles have the same measure.
In this case, we have two pairs of vertical angles. Let's label the angles for clarity:
Angle 1: 140° (given)
Angle 2: ?
Angle 3: ?
Angle 4: ?
Since Angle 1 is 140°, we know that Angle 3, which is vertical to Angle 1, must also be 140°. Therefore, Angle 3 = 140°.
Similarly, Angle 2 and Angle 4 are the other pair of vertical angles. Since Angle 2 is opposite to Angle 1 (140°), it must also be 140°. Therefore, Angle 2 = 140°.
Finally, to find Angle 4, we can use the fact that the sum of angles along a straight line is 180°. Since Angle 2 = 140°, we can subtract it from 180° to find Angle 4.
Angle 4 = 180° - 140° = 40°.
In summary, the measures of the three remaining angles are:
Angle 1: 140°
Angle 2: 140°
Angle 3: 140°
Angle 4: 40°