Question

Refer to the photo

The figure is not draw to scale. Points B, C, and D are collinear

Answer 1

Answer: m∠D = 106°

Step-by-step explanation:

         Since these two triangles are congruent (given by ΔABC ≅ ΔDEC) they are equal to each other and therefore their angles will also be equal to each other. We also have vertical angles, ∠ACB ≅ ∠DCE. These will be congruent as well.

         With this information in mind, we will solve for x.

                   ΔABC ≅ ΔDEC

                   ∠ABC ≅ ∠DEC

                   2x + 40 = 5x + 10

                   -3x = -30

                   x = 10

         Next, we will find m∠DCE and m∠ACB (so we can find m∠DCE) using this value of x and substitution.

                   m∠DCE = 5x° + 10° = 5(10)° + 10° = 50° + 10° = 60°

                   m∠ACB = x° + 4° = (10)° + 4° = 14°

                   ∠ACB ≅ ∠DCE, so m∠DCE = 14°

         Next, a triangle's interior angles add up to 180 degrees. We can create an equation to solve for m∠D.

                   m∠D = 180° - 60° - 14°

                   m∠D = 106°

Answer 2

Answer:

$\text{}71.5^\circ$

Step-by-step explanation:

$1.\ \angle\text{B = }\angle\text{D}=(2x+40)^\circ\ \ \ [\text{Corresponding angles of congruent triangles .}\\\text{}\quad\text{are congruent.]}\\\\\text{2. In }\triangle\text{CDE},\\\text{}\quad\angle\text{DCE}+\angle\text{D}+\angle\text{E}=180^\circ\ \ \ [\text{Sum of angles of triangle is 180}^\circ.]\\\text{or, }(x+4)^\circ+(2x+40)^\circ+(5x+10)^\circ=180^\circ\\\text{or, }8x+54^\circ=180^\circ\\\text{or, }8x=126^\circ\\\text{or, }x=15.75^\circ$

$\text{3. m}\angle\text{D}=(2x+40)^\circ=(2\times15.75+40)^\circ=71.5^\circ$