Question

question
the measures of the angles of a triangle are shown in the figure below. find the measure of the smallest angle.
105°
(5x+14)°
(6x+17)°
answer attempt 1 out of 2
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Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \(105 + (6x + 17) + (5x + 14) = 180\).

Step2: Simplify the equation

Combine like terms: \(105 + 17 + 14 + 6x + 5x = 180\) → \(136 + 11x = 180\).

Step3: Solve for \(x\)

Subtract 136: \(11x = 180 - 136 = 44\) → \(x = \frac{44}{11} = 4\).

Step4: Find each angle

• \(6x + 17 = 6(4) + 17 = 24 + 17 = 41^\circ\)
• \(5x + 14 = 5(4) + 14 = 20 + 14 = 34^\circ\)
• The third angle is \(105^\circ\).

Step5: Identify the smallest angle

Compare \(34^\circ\), \(41^\circ\), and \(105^\circ\). The smallest is \(34^\circ\).

Answer:

\(34^\circ\)