Questions: Find the measure of each angle indicated. 9) m angle S

Find the measure of each angle indicated. 9) m angle S
Transcript text: Find the measure of each angle indicated. 9) $m \angle S$
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Solution

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Solution Steps

Step 1: Identify the given angles and expressions

The given angles in the quadrilateral are:

  • ∠R = 70°
  • ∠Q = 113°
  • ∠S = 12x - 4
  • ∠T = 12x + 13
Step 2: Use the sum of interior angles of a quadrilateral

The sum of the interior angles of a quadrilateral is always 360°. Therefore, we can set up the equation: \[ \angle R + \angle Q + \angle S + \angle T = 360° \]

Step 3: Substitute the given values and expressions into the equation

Substitute the given angles and expressions into the equation: \[ 70° + 113° + (12x - 4) + (12x + 13) = 360° \]

Step 4: Simplify the equation

Combine like terms: \[ 70 + 113 + 12x - 4 + 12x + 13 = 360 \] \[ 70 + 113 - 4 + 13 + 24x = 360 \] \[ 192 + 24x = 360 \]

Step 5: Solve for x

Isolate x by subtracting 192 from both sides: \[ 24x = 360 - 192 \] \[ 24x = 168 \] \[ x = \frac{168}{24} \] \[ x = 7 \]

Step 6: Find the measure of ∠S

Substitute x = 7 back into the expression for ∠S: \[ \angle S = 12x - 4 \] \[ \angle S = 12(7) - 4 \] \[ \angle S = 84 - 4 \] \[ \angle S = 80° \]

Final Answer

The measure of ∠S is 80°.

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