Two lines intersect, forming two pairs of vertical angles. One of these angles is 110°. What are the measures of the three remaining angles?
a 70, 70, 180
b 70, 70, 70
c 110, 70, 70
d 110, 110, 70
is it d?
it was c) 110,70,70
No, it is not option d. The correct answer is option c.
When two lines intersect, the pairs of vertical angles are congruent. This means that if one angle measures 110°, then the opposite angle will also measure 110°.
So, the measures of the three remaining angles are:
- The angle opposite the 110° angle is also 110°.
- The remaining two angles are vertical angles and are congruent to each other. Therefore, they each measure 70°.
Thus, the correct answer is option c: 110, 70, 70.
To find the measures of the three remaining angles, we need to use the fact that vertical angles are congruent.
Vertical angles are formed when two lines intersect. They are opposite each other and share the same vertex. In this case, we have two pairs of vertical angles.
Let's call the angle that measures 110° as angle A.
Since vertical angles are congruent, the angle opposite angle A (let's call it angle B) will also measure 110°.
Now we have two angles that we know the measure of: angle A = 110° and angle B = 110°.
The sum of the measures of the angles in a straight line is always 180°. Since angle A and angle B are in a straight line, the sum of their measures is 180°.
To find the measure of the remaining angle, let's call it angle C, we subtract the sum of the measures of angle A and angle B from 180°:
Angle C = 180° - (angle A + angle B) = 180° - (110° + 110°) = 180° - 220° = -40°.
The measure of angle C is -40°, which is not possible for an angle. Therefore, none of the given options (a, b, c, d) are correct.