Question

In abc, if ac is congruent to cb, angle a = (3x 18), angle b = (7x-58), and angle c = (2x-8), find the value of x and the measure of each angle

Answer 1

To solve for x, set up an equation using the sum of triangle angles equals 180 degrees, then substitute and solve for x. After finding x to be 19, calculate each angle using the given expressions.

Step-by-step explanation:

The question involves finding the value of x in a triangle where the sides AC and CB are congruent and the angles are defined by algebraic expressions in terms of x. To solve this, we need to use the fact that the sum of angles in a triangle is 180 degrees.

We set up an equation with the sum of the angles as follows:

1. Angle A = 3x + 18
2. Angle B = 7x - 58
3. Angle C = 2x - 8

Summing the angles, we get (3x + 18) + (7x - 58) + (2x - 8) = 180. Simplifying this equation:

3x + 7x + 2x + 18 - 58 - 8 = 180
12x - 48 = 180
12x = 228
x = 19

Now we can find the measures of each angle:

• Angle A = 3(19) + 18 = 75 degrees
• Angle B = 7(19) - 58 = 75 degrees
• Angle C = 2(19) - 8 = 30 degrees

Note that angle A is equal to angle B, confirming that AC is indeed congruent to CB.