Question

terior angles
m∠bec=

m∠abc=

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. In triangle \(BEC\), \(\angle ECD = 93^{\circ}\) is an exterior angle. So, \(2x=x + 93^{\circ}\).

Step2: Solve for \(x\)

Subtract \(x\) from both sides of the equation \(2x=x + 93^{\circ}\). We get \(2x−x=x−x + 93^{\circ}\), which simplifies to \(x = 93^{\circ}\).

Step3: Find \(m\angle BEC\)

Since \(m\angle BEC=x\), then \(m\angle BEC = 31^{\circ}\).

Step4: Find \(m\angle ABC\)

Since \(m\angle ABC = 2x\), substitute \(x = 31^{\circ}\). So, \(m\angle ABC=2\times31^{\circ}=62^{\circ}\).

Answer:

\(m\angle BEC = 31^{\circ}\), \(m\angle ABC = 62^{\circ}\)