Question

what is m∠1? (5x - 10)° 40° 3x°

Explanation:

Step1: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, in the triangle, we have the equation \(40^{\circ}+3x^{\circ}+(5x - 10)^{\circ}=180^{\circ}\).

Step2: Combine like - terms

Combine the \(x\) terms and the constant terms: \((3x + 5x)+(40-10)=180\), which simplifies to \(8x + 30=180\).

Step3: Isolate the variable \(x\)

Subtract 30 from both sides of the equation: \(8x=180 - 30\), so \(8x=150\). Then divide both sides by 8: \(x=\frac{150}{8}=\frac{75}{4}=18.75\).

Step4: Find the measure of the exterior angle

The exterior angle \(\angle1\) is equal to the sum of the two non - adjacent interior angles of the triangle. So, \(\angle1=40^{\circ}+3x^{\circ}\). Substitute \(x = 18.75\) into the equation: \(3x=3\times18.75 = 56.25\), and \(\angle1=40 + 56.25=96.25^{\circ}\).

Answer:

\(96.25^{\circ}\)