When two lines intersect, and the sum of three of the four angles formed is equal to 270°, then each angle measure 90° each.
What are the angles formed when two lines intersect?
When two lines intersect, suppose AB and CD, we get adjacent angles and vertically opposite angles.
- Adjacent angles: The angles on the same side of a line are adjacent to each other. Adjacent angles are always supplementary, that is, their sum is always equal to 180°.
- Vertically opposite angles: The angles on the opposite side of a line are vertically opposite to each other. Vertically opposite angles are always equal.
In the figure, ∠AOC and ∠COB, ∠COB and ∠BOD, ∠BOD and ∠DOA, and ∠DOA and ∠AOC, are adjacent pairs, whereas, ∠AOC and ∠BOD, and ∠COB and ∠DOA are vertically opposite pairs.
Also, the sum of the four angles formed by the intersection of the two lines is 360°.
How to solve the question?
In the question, we are asked to find the angles formed by two intersecting lines, if the sum of three of the four angles is equal to 270°.
We know that when two lines intersect, the sum of the four angles formed is 360°.
Given the sum of three of the four angles is 270°, the measure of the fourth angle can be calculated as 360° - 270° = 90°.
When one angle is 90°, the angle opposite to it is also 90°, as vertically opposite angles have equal measure.
The other two angles are both adjacent to these angles, that is, the sum of each with one angle is 180°, as adjacent angles are supplementary.
Thus, the other two angles measure 180° - 90° = 90° each.
Thus, when two lines intersect, and the sum of three of the four angles formed is equal to 270°, then each angle measure 90° each.
Learn more about the angles formed by intersecting lines at
https://brainly.com/question/15318840
#SPJ2
