Solve for x in the diagram below.

Question

asked Aug 22, 2023 88.1k views

2 Answers

Jaeho · Answer 1 · 2023-08-24T02:23:54+0000

Answer:

x = 20

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

William Revelle · Answer 2 · 2023-08-27T01:58:11+0000

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:

$\implies x + 2x + (x + 10) = 90\°$

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

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

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

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

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

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

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

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