To find the measure of angle CYL, we utilize the exterior angle theorem and the angle sum property of triangles. By setting up and solving equations with the given angle expressions, the measure of angle CYL is calculated to be approximately 30.7 degrees.
Step-by-step explanation:
The student is asked to find the measure of angle CYL in a triangle YCL with the following given information:
Angle Y = (5x + 3)°
Angle C = (4x + 26)°
Exterior angle YLR = (7x + 7)°
To find the measure of angle CYL, we can use the fact that the sum of the interior angles of a triangle is 180° and the exterior angle theorem, which states that an exterior angle is equal to the sum of the two opposite interior angles.
First, we write the equation based on the exterior angle theorem:
Angle YLR = Angle Y + Angle CYL
Substituting the given expressions, we get:
7x + 7 = (5x + 3) + angle CYL
Solving for angle CYL:
Angle CYL = (7x + 7) - (5x + 3)
Angle CYL = 2x + 4.
Next, we use the angle sum property for the triangle to find the value of x:
180 = (5x + 3) + (4x + 26) + angle CYL
Substituting the expression for angle CYL:
180 = (5x + 3) + (4x + 26) + (2x + 4)
Combining like terms:
180 = 11x + 33
Solving for x:
x = (180 - 33) / 11
x = 13.36
Now, substituting x back into the expression for angle CYL:
Angle CYL = 2(13.36) + 4
Angle CYL = 30.7°
Therefore, the measure of angle CYL is approximately 30.7°.