Question

the measures of the angles of a triangle are shown in the figure below. find the measure of the smallest angle.
(7x-16)°
115°
(x+17)°
answer attempt 1 out of 2
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Explanation:

Step1: Use the triangle - angle sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \((x + 17)+(7x-16)+115=180\).
Simplify the left - hand side: \(x+17 + 7x-16+115=(x + 7x)+(17-16 + 115)=8x+116\).
The equation becomes \(8x+116 = 180\).

Step2: Solve for \(x\)

Subtract \(116\) from both sides of the equation: \(8x=180 - 116\).
\(8x=64\).
Divide both sides by \(8\): \(x=\frac{64}{8}=8\).

Step3: Find the measures of the angles

For the angle \((x + 17)^{\circ}\), substitute \(x = 8\): \(x+17=8 + 17=25^{\circ}\).
For the angle \((7x-16)^{\circ}\), substitute \(x = 8\): \(7x-16=7\times8-16=56 - 16=40^{\circ}\).
The three angles are \(25^{\circ}\), \(40^{\circ}\), and \(115^{\circ}\).

Answer:

\(25^{\circ}\)