Questions: Example 2: Find x and the measures of all of the angles

Example 2: Find x and the measures of all of the angles
Transcript text: Example 2: Find $x$ and the measures of all of the angles
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Solution

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Solution Steps

Step 1: Set up the equation

The given angles are supplementary, meaning their sum is 180 degrees. Therefore, we can set up the equation: \[ (2x + 9) + 115 = 180 \]

Step 2: Simplify the equation

Combine like terms: \[ 2x + 124 = 180 \]

Step 3: Solve for x

Subtract 124 from both sides: \[ 2x = 56 \] Divide by 2: \[ x = 28 \]

Step 4: Find the measure of angle 1

Substitute \( x = 28 \) back into the expression for the angle: \[ 2x + 9 = 2(28) + 9 = 56 + 9 = 65 \]

Step 5: Find the measure of angle 2

Since angle 2 is given as 115 degrees, we already know its measure.

Final Answer

  • \( x = 28 \)
  • \( \angle 1 = 65^\circ \)
  • \( \angle 2 = 115^\circ \)
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