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
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.
To prove that angle ABC is congruent to angle D, we need to show that their measures are equal.
Given:
Angle 1 = (x + 7) degrees
Angle 2 = (2x - 3) degrees
Angle ABC = (x^2) degrees
Angle D = (5x - 4) degrees
We can start by setting up an equation based on the given information.
Angle ABC = Angle D
Since Angle ABC is measured in terms of x^2 and Angle D is measured in terms of 5x - 4, we can equate them:
x^2 = 5x - 4
Now we will solve the equation to find the value of x.
x^2 - 5x + 4 = 0
Factoring the above quadratic equation, we have:
(x - 1)(x - 4) = 0
From this, we obtain two possible values for x: x = 1 and x = 4.
Next, we substitute these values back into the given expressions to find the measures of the angles.
For x = 1:
Angle ABC = (1^2) = 1 degree
Angle D = (5(1) - 4) = 1 degree
For x = 4:
Angle ABC = (4^2) = 16 degrees
Angle D = (5(4) - 4) = 16 degrees
Since the measures of Angle ABC and Angle D are equal for both values of x, we can conclude that angle ABC is congruent to angle D.