Question

Given angle 1 = (x + 7)degree, angle 2 = *(2x -3)degree, angle ABC = (x 2nd power) degree, angle D = (5x - 4)degree. Show that angle ABC congruent to angle D

Answer 1

To prove that angle ABC is congruent to angle D, we need to show that their measures are equal.

Given:

Angle 1 = (x + 7) degree
Angle 2 = (2x - 3) degree
Angle ABC = (x^2) degree
Angle D = (5x - 4) degree

We can start by setting up an equation to represent the measure of angle ABC and angle D:

x^2 = 5x - 4

Now, let's solve for x.

x^2 - 5x + 4 = 0

Factoring the equation, we get:

(x - 1)(x - 4) = 0

Setting each factor equal to zero:

x - 1 = 0 or x - 4 = 0

Solving for x in each equation:

x = 1 or x = 4

Therefore, there are two possible values for x, which are x = 1 and x = 4.

Now, let's substitute these values into the given angles to find the measures:

For x = 1:
Angle ABC = (1^2) degree = 1 degree
Angle D = (5(1) - 4) degree = 1 degree

For x = 4:
Angle ABC = (4^2) degree = 16 degrees
Angle D = (5(4) - 4) degree = 16 degrees

In both cases, the measure of angle ABC is equal to the measure of angle D.

Therefore, angle ABC is congruent to angle D.