One of the angles formed by two intersecting lines is 50° less than the other. Find the measure of all angles.

When two lines intersect, they form two pairs of vertical angles which are equal. In this problem, let's define one angle as:

Let angle A be x degrees.

Then, the other angle, which is 50° less than angle A, is x − 50° .


Since these two angles form a linear pair (angles on a straight line) when added together, their sum should be 180°.
Step-by-step solution:

Equation Setup:
The sum of angles in a linear pair equals 180°:
x + ( x − 50° ) = 180°

Combine Like Terms:
2 x − 50° = 180°

Solve for x :
Add 50° to both sides of the equation:
2 x = 230°
Divide both sides by 2:
x = 115°

Find the Other Angle:
The other angle is x − 50° :
115° − 50° = 65°


Angles' Measures:

One angle is 115° and the other is 65°.

Verification:

Both are complementary angles that sum up to 180° (115° + 65° = 180°), confirming the solution is consistent and correct.

Thus, the measures of the angles formed by the intersecting lines are 115° and 65°.

Answered by SophiaElizab | 2025-07-22

The angles formed by the intersecting lines are 115 degrees and 65 degrees. One angle is 50 degrees less than the other. Their measures add up to 180 degrees, confirming the solution is valid.
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Answered by SophiaElizab | 2025-08-26