The Truth about Acute Angles in Intersecting Lines: Understanding the Relationship Between Angle Measures

if one of the angles formed by two intersecting lines is acute, then the other three anglesformed are also acute

To understand why this statement is true, let’s consider two intersecting lines, line AB and line CD

To understand why this statement is true, let’s consider two intersecting lines, line AB and line CD. When two lines intersect, they form four angles.

Let’s label the angles as follows:
– Angle 1: The angle formed by line AB and line CD.
– Angle 2: The angle formed by line AB and a different line that intersects it.
– Angle 3: The angle formed by line CD and a different line that intersects it.
– Angle 4: The angle formed by the two other lines that intersect each other.

Now, let’s assume that angle 1 is acute. An acute angle is an angle that measures less than 90 degrees.

Now, we can see that angle 1 and angle 4 are opposite angles formed by intersecting lines. So, if angle 1 is acute, then angle 4 must also be acute because they are congruent angles.

Next, let’s consider angles 2 and 3. These angles are adjacent angles and share a common vertex (the point where the two intersecting lines meet). When formed by intersecting lines, adjacent angles are always supplementary, meaning that the sum of their measures is 180 degrees.

Now, if angle 1 is acute (measures less than 90 degrees), angles 2 and 3 cannot both be obtuse or right angles (measuring 90 degrees or more) because that would make their sum greater than 180 degrees. So, the only possibility is that angles 2 and 3 are also acute (measuring less than 90 degrees).

Therefore, if angle 1 is acute, angle 4 and angles 2 and 3 must also be acute. So, the statement “if one of the angles formed by two intersecting lines is acute, then the other three angles formed are also acute” is true.

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