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Solve for x in the diagram below.

Solve for x in the diagram below.-example-1

2 Answers

4 votes

Answer:

x = 20

Explanation:

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

User Jaeho
by
8.5k points
3 votes

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 (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.

User William Revelle
by
7.4k points

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