Question

Solve for x in the diagram below.

Answer 1

Step-1: Understanding the Diagram

Since we can see the "square" at the bottom left corner of the angle, the square indicates that the angle is a right angle (which measures 90°).

We can also see three smaller angles forming the right angle. Therefore, the sum of the measure of the smaller angles = 90°.

According to the diagram, the measures of the smaller angles are x°, 2x°, and (x + 10)° respectively. Then we get the following equation:

$\implies x + 2x + (x + 10) = 90\°$

Step-2: Solving the equation obtained in step-1

Here, we had the equation: $\underline{x + 2x + (x + 10) = 90\°}$

$\implies x + 2x + x + 10 = 90\°$              $\text{(Ope} \text{ning the parentheses)}$

$\implies 4x + 10 = 90\°$                             $\text{(Combining like terms)}$

$\implies 4x + 10 - 10 = 90 - 10$          $\text{(Subtracting 10 on both sides)}$

$\implies 4x = 80$                                    $\text{(Simplifying both sides)}$

$\implies \dfrac{4x}{4} = \dfrac{80}{4} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \text{(Dividing 4 on both sides)}$                            

$\implies \boxed{x = 20}$                                      $\text{(Simplifying both sides)}$

Therefore, the value of x, in the diagram provided, is 20.

Answer 2

Answer:

x = 20

Step-by-step explanation:

x°

2x°

(x + 10)°

little box on the bottom left means this is a right angle which is 90°

add up all the angles and make it equal to 90°

( x° + 2x° + (x + 10)° ) = 90°

4x + 10 = 90

4x = 80

x = 20