Three supplementary angles are ∠KLM=x+30°, ∠MLN=60°, ∠NLP=2x°. What is an equation to solve for the unknown angle value? Write the equation in simplest terms.
Equation: x + 30 + 60 + 2x = 180
Simplified equation: 3x + 90 = 180
3x = 90
x = 30
To find the unknown angle value, we can set up an equation using the fact that the sum of all three supplementary angles is equal to 180 degrees.
The sum of ∠KLM, ∠MLN, and ∠NLP is equal to 180°, so we can write the equation as:
∠KLM + ∠MLN + ∠NLP = 180°
If we substitute the given angle values in terms of x into the equation, we get:
(x + 30°) + 60° + (2x°) = 180°
Now, we simplify the equation:
x + 30° + 60° + 2x° = 180°
Combining like terms:
3x + 90° = 180°
To isolate x, we subtract 90° from both sides:
3x = 180° - 90°
3x = 90°
Finally, we divide both sides by 3 to solve for x:
x = 90°/3
Simplifying:
x = 30°
Therefore, the unknown angle value is 30 degrees.
To find the unknown angle value, we need to set up an equation that represents the fact that the three angles are supplementary, meaning their sum is 180°.
We have three angles: ∠KLM, ∠MLN, and ∠NLP. Let's find their sum:
∠KLM + ∠MLN + ∠NLP = (x+30°) + 60° + 2x°
Simplifying the equation:
x + 30° + 60° + 2x° = 180°
Combining like terms:
3x + 90° = 180°
Now, let's solve for x. We'll start by isolating the variable:
3x = 180° - 90°
3x = 90°
Divide both sides by 3:
x = 90° / 3
x = 30°
So, the unknown angle value, x, is equal to 30°.