Question

Choose the correct values from the diagram. Then, solve for x:

Angle EAF = 4x + 10
Angle FAL = 3x + 15

The values:

4x + 10
3x + 15
10
5
7
8
x =
Angle EAF =
Angle FAL =

Please fill in the values and provide the solutions for x, Angle EAF, and Angle FAL.

Answer 1

To find the value of x given the angles EAF and FAL in an equation, set up and solve the equation based on the fact that these angles combine to form a straight line of 180°. This results in x having a value of approximately 22.14, with angle EAF being approximately 98.86 degrees and angle FAL being approximately 81.14 degrees.

Step-by-step explanation:

Solving for x in Angle Relationships

To solve for x when given the angles EAF and FAL as 4x + 10 and 3x + 15 respectively, we work under the assumption that EAF and FAL are adjacent angles that form a straight line. A straight line measures 180°, so we can set up the following equation:

4x + 10 + 3x + 15 = 180

Combining like terms, we get:

7x + 25 = 180

Subtracting 25 from both sides gives us:

7x = 155

Dividing both sides by 7, we find:

x = 155 ÷ 7

x = 22.14

Now, to find the measure of angle EAF:

Angle EAF = 4(22.14) + 10

Angle EAF = 98.857 degrees, approximately 98.86 degrees

And for angle FAL:

Angle FAL = 3(22.14) + 15

Angle FAL = 81.143 degrees, approximately 81.14 degrees