Question

1. the angle measures of a triangle are 7x + 14 degrees, 8x + 1 degress, and 5x + 5 degrees. which of the following is not one of the angles measres of the triangle? a) 45 b) 40 c) 70 d) 65

Explanation:

Step1: Use the triangle - angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \((7x + 14)+(8x + 1)+(5x + 5)=180\).

Step2: Combine like terms

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Step3: Solve for \(x\)

Subtract \(20\) from both sides: \(20x=180 - 20=160\). Then divide both sides by \(20\): \(x=\frac{160}{20}=8\).

Step4: Find each angle measure

• For the first angle: \(7x + 14\), substitute \(x = 8\). \(7\times8+14=56 + 14=70\).
• For the second angle: \(8x + 1\), substitute \(x = 8\). \(8\times8+1=64 + 1=65\).
• For the third angle: \(5x + 5\), substitute \(x = 8\). \(5\times8+5=40 + 5=45\).

Answer:

B. \(40\)