The sum of two angles formed by the intersection of two lines is 114 degrees. Find the measures of all angles.
Let's call the two angles formed by the intersection of the two lines angle A and angle B.
We know that the sum of these two angles is 114 degrees.
So, we can write the equation:
A + B = 114
However, we need more information to find the measures of each angle individually. Are there any other conditions or relationships provided?
To find the measures of all angles, we need to consider the properties of intersecting lines and the relationship between their angles.
When two lines intersect, they form four angles. Let's label these angles as follow:
Angle 1 (α) ---------------
Angle 2 (β) ---------------
Angle 3 (γ) ---------------
Angle 4 (δ) ---------------
According to the problem, we are given that the sum of two angles formed by the intersection of the lines is 114 degrees. Let's assume these two angles are α and β.
Step 1: Write down the given information:
α + β = 114 degrees
Step 2: Understand the relationship between opposite angles:
Angles α and γ are opposite angles, as well as angles β and δ.
The relationship between opposite angles states that they are equal. Therefore, we can write:
α = γ
β = δ
Step 3: Calculate the value of an angle using the relationship between opposite angles:
Since α + γ = 180 degrees (they form a straight line), we can substitute α with γ:
α + α = 2α = 180 degrees
Solve for α:
2α = 180 degrees
α = 180 degrees / 2
α = 90 degrees
Step 4: Calculate the value of β using the given information:
Since α + β = 114 degrees, we can substitute α with its value:
90 degrees + β = 114 degrees
β = 114 degrees - 90 degrees
β = 24 degrees
Step 5: Determine the measures of the remaining angles using the relationship between opposite angles:
γ = α = 90 degrees
δ = β = 24 degrees
So, the measures of the angles are as follows:
α = 90 degrees
β = 24 degrees
γ = 90 degrees
δ = 24 degrees