If two lines intersect and one angle measures 35°, what are the measures of the other angles?
What is 180-35 ?
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If two lines intersect, they form four angles. Let's call the angle that measures 35° "angle A".
By vertical angles theorem, opposite angles formed by the intersection of two lines are congruent. Therefore, there is another angle, let's call it "angle B", that is also 35°.
Now, we know that the sum of the measures of the interior angles on the same side of a transversal is 180°. Since angles A and B are on the same side of the transversal, they will have a supplementary angle, which we'll call "angle C".
To find the measure of angle C, we subtract the sum of angles A and B from 180°: C = 180° - (35° + 35°) = 180° - 70° = 110°.
Therefore, the measures of the other angles are:
Angle A = 35°
Angle B = 35°
Angle C = 110°
To find the measures of the other angles when two lines intersect and one angle measures 35°, we need to understand some concepts related to angles formed by intersecting lines.
When two lines intersect, they create four angles known as vertical angles, which are opposite each other. Vertical angles are always congruent, meaning they have the same measure. Therefore, we can conclude that the angle opposite the given angle of 35° also measures 35°.
In addition to the vertical angles, when two lines intersect, they form two pairs of adjacent angles known as linear pairs. Linear pairs are supplementary, meaning the sum of their measures is 180°.
So, to find the measures of the other angles, we need to determine the measure of the linear pair with the given angle of 35°. Since the sum of the measures of adjacent angles forming a straight line is 180°, we subtract 35° from 180° to find the measure of the other angle:
180° - 35° = 145°
Therefore, the measure of the other angle formed by the intersection of the two lines is 145°.