One of four angles formed by two intersecting line is 65 . find the remaining 3 angles ?

Question

Answer

1st angle - 65 degree 3rd angle - 65 degree ( vertically.     opposite angles)2nd angle - 180 - 65 degree=115 degree. ( linear pair) 4th angle - 115 degree  ( vertically opposite angles)

Answer

So simpleFind by using some properties1. Vertically opposite angle2. Linear pair axiom

Answer

Analysis:
To find the remaining 3 angles formed by two intersecting lines when one angle is given as 65 degrees, we can use the properties of angles formed by intersecting lines.

Vertical Angles:
- Vertical angles are congruent, meaning they have the same measure.
- When two lines intersect, they form two pairs of vertical angles.
- Therefore, the angle opposite the given 65-degree angle is also 65 degrees.

Linear Pair:
- A linear pair is formed when two lines intersect, and the adjacent angles add up to 180 degrees.
- Since one angle is given as 65 degrees, the linear pair angle can be found by subtracting 65 from 180.
- Therefore, the linear pair angle is 180 - 65 = 115 degrees.

Corresponding Angles:
- Corresponding angles are equal when a transversal intersects two parallel lines.
- In this case, since the lines are intersecting, corresponding angles are not equal.
- However, we can find the fourth angle by subtracting the sum of the three known angles from 360 degrees.
- Therefore, the fourth angle is 360 - (65 + 65 + 115) = 115 degrees.

Summary:
- The three remaining angles are 65 degrees, 65 degrees, and 115 degrees, with the fourth angle also measuring 115 degrees.
- These angles are formed by two intersecting lines and follow the properties of vertical angles, linear pairs, and corresponding angles.

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