Question

If m∠COL=X+41, m∠ROC=X−78, and m∠ROL=95°, find the value of x.

a) Solving for x
b) Applying angle relationships
c) Using angle measures to determine x
d) All of the above

Answer 1

The value of x is found by using the property that the sum of angles in a triangle equals 180°. By setting up an equation with the given angle measures and solving for x, we find that the value of x is 61°.

Step-by-step explanation:

The student is asked to find the value of x given the angles m∠COL, m∠ROC, and m∠ROL in a geometric figure. Since the sum of the angles in a triangle equals 180°, we can set up an equation with the given angle measures:

• m∠COL = x + 41°
• m∠ROC = x - 78°
• m∠ROL = 95°

Add all the angles to set them equal to 180°:

(x + 41°) + (x - 78°) + 95° = 180°

Simplify the equation:

2x + 41° - 78° + 95° = 180°

2x + 58° = 180°

Subtract 58° from both sides:

2x = 122°

Divide by 2:

x = 61°

Therefore, the value of x is 61 degrees.