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]
