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Answer:

∠ ABC = 50°

Step-by-step explanation:

Given that Δ CDE is equilateral , then the 3 interior angles are congruent (equal ), that is

sum of the 3 angles in a triangle is 180° , so

∠ C = ∠ D = ∠ E = 60°

note that ∠ D = ∠ BDA in Δ ABD

Given ∠ EAB = 70° = ∠ DAB , in Δ ABD , then

∠ ABC + ∠ ∠ DAB + ∠ BDA = 180°

∠ ABC + 70° + 60° = 180°

∠ ABC + 130° = 180° ( subtract 130° from both sides )

∠ ABC = 50°

Answer:

m∠ABC = 50°

Step-by-step explanation:

An equilateral triangle is a triangle in which all three interior angles are equal, each measuring 60°. Therefore, given that triangle DEC is equilateral:

[tex]\sf m\angle CDE = 60^{\circ}[/tex]

Triangles DAB and DEC share the common vertex D. Therefore, ∠BDA ≅ ∠CDE. Since m∠CDE = 60°, then:

[tex]\sf m\angle BDA= 60^{\circ}[/tex]

The interior angles of a triangle sum to 180°. So, in triangle DAB:

[tex]\sf m\angle DAB + m\angle ABD + m\angle BDA = 180^{\circ}[/tex]

Given that m∠DAB = 70°, we can substitute this along with m∠BDA = 60° into the equation and solve for m∠ABD:

[tex]\sf 70^{\circ} + m\angle ABD + 60^{\circ} = 180^{\circ}\\\\m\angle ABD + 130^{\circ} = 180^{\circ}\\\\m\angle ABD = 180^{\circ} - 130^{\circ}\\\\m\angle ABD = 50^{\circ}[/tex]

As angle ABC is also angle ABD, then the value of angle ABC is:

[tex]\Large\boxed{\boxed{\sf m\angle ABC = 50^{\circ}}}[/tex]

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