Question

4. Based on the triangle sum theorem, solve for x.

Answer 1

x = 10

Explanation:

180 = 90 + 40 + (4x + 10)

180 = 130 + (4x + 10)

4x + 10 = 180 - 130

4x + 10 = 50

4x = 50 - 10

4x = 40

x = 40/4

x = 10

Answer 2

x = 10

Explanation:

An euclidean triangle is defined to have sum of all 3 interior angles equal to 180°.

In the given triangle, we know three measurement:

• 4x+10
• 40°
• 90°

You may be wondering, where does 90° come from. The answer is you can find it by looking if a triangle has a little square symbol or not. If it does, the measurement will always be 90°.

Now since we know that sum of 3 interior angles must equal to 180° in euclidean triangle. Therefore, sum up three of measurement then set to 180°.

`\displaystyle{90 + 4x+10 + 40= 180}`

Evaluate and solve for the x-variable:

`\displaystyle{90 + 4x+10 + 40= 180}\\\\\displaystyle{4x+140 = 180}\\\\\displaystyle{4x=180-140}\\\\\displaystyle{4x=40}\\\\\displaystyle{x=10}`

Therefore, the value of x is 10