Question

i can... use the triangle sum theorem and the exterior angle theorem to find measures of angles. (gr1.3) find ( mangle jkm ).

Explanation:

Step1: Apply the Exterior Angle Theorem

The Exterior Angle Theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(2x - 3=x + 58\).

Step2: Solve for \(x\)

Subtract \(x\) from both sides of the equation: \(2x-x-3=x - x+58\), which simplifies to \(x-3 = 58\). Then add 3 to both sides: \(x=58 + 3=61\).

Step3: Find \(m\angle JKM\)

Substitute \(x = 61\) into the expression for \(m\angle JKM=(2x - 3)^{\circ}\). So, \(m\angle JKM=(2\times61-3)^{\circ}=(122 - 3)^{\circ}=119^{\circ}\).

Answer:

\(119^{\circ}\)