Question

m∠bec =
m∠abc =
(and a diagram with points a, b, c, d, e, f, angles labeled 2x°, x°, 93°)

Explanation:

Step1: Identify the triangle's angle sum

In triangle \( BEC \), we know that the exterior angle at \( C \) (which is \( 93^\circ \)) is equal to the sum of the two non - adjacent interior angles. So, \( 93^\circ=x + 2x\).

Step2: Solve for \( x \)

Simplify the equation \( 93 = 3x\). Divide both sides by 3: \(x=\frac{93}{3}=31\).

Step3: Find \( m\angle BEC \)

Since \( m\angle BEC=x^\circ \), substituting \( x = 31 \), we get \( m\angle BEC = 31^\circ\).

Step4: Find \( m\angle ABC \)

Since \( m\angle ABC = 2x^\circ \), substituting \( x = 31 \), we get \( m\angle ABC=2\times31 = 62^\circ\).

Answer:

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