Respuesta :

MrRoyal

Answer:

[tex]x = 18[/tex]

[tex]\angle A = 166[/tex]

Step-by-step explanation:

The question is properly presented in the attachment.

Given

[tex]\angle A = 7x + 40[/tex]

[tex]\angle B = 3x + 112[/tex]

Required

Solve for x and  [tex]\angle A[/tex]

From the attachment [tex]\angle A[/tex] and [tex]\angle B[/tex] are vertically opposite.

This means that:

[tex]\angle A[/tex] = [tex]\angle B[/tex]

Substitute values for [tex]\angle A[/tex] and [tex]\angle B[/tex]

[tex]7x + 40 = 3x + 112[/tex]

Collect Like Terms

[tex]7x -3x = 112 - 40[/tex]

[tex]4x = 72[/tex]

Make x the subject

[tex]x = \frac{72}{4}[/tex]

[tex]x = 18[/tex]

Substitute 18 for x in [tex]\angle A = 7x + 40[/tex]

[tex]\angle A = 7 * 18 + 40[/tex]

[tex]\angle A = 166[/tex]

Ver imagen MrRoyal
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

7*x+40-(3*x+112)=0

Step by step solution :

STEP
1
:
Pulling out like terms

1.1 Pull out like factors :

4x - 72 = 4 • (x - 18)

Equation at the end of step
1
:

STEP
2
:

Equations which are never true:

2.1 Solve : 4 = 0

This equation has no solution.
A a non-zero constant never equals zero.

Solving a Single Variable Equation:

2.2 Solve : x-18 = 0

Add 18 to both sides of the equation :
x = 18

One solution was found :
x = 18

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