Respuesta :

Answer:

Step-by-step explanation:

Since, ΔBCM ≅ ΔZYR,

∠B ≅ ∠Z

∠C ≅ ∠Y

∠M ≅ ∠R

And BC ≅ ZY

CM ≅ YR

BM ≅ ZR

a). CM = YR = 11 m

b). BM = RZ = 15 m

c). YZ = BC = 8 m

d). m∠B = m∠Z = 45°

e). m∠M = 180° - [m(∠B) + m(∠C)]

              = 180° - (45 + 103)°

              = 180° - 148°

              = 32°

f). m∠Y = m∠C = 103°

MrRoyal

Congruent triangles have equal corresponding sides and angles

  • The measure of the side lengths are:[tex]YZ =8[/tex], [tex]BM =15[/tex] and [tex]CM = 11[/tex]
  • The measure of the angles are [tex]\angle B =45[/tex], [tex]\angle Y =103[/tex] and [tex]\angle M = 32[/tex]

The given parameter is:

[tex]\triangle BCM \cong \triangle ZYR[/tex]

This means that triangle BCM and ZYR are congruent.

So, we have the following congruent sides

[tex]YZ =CB[/tex]

[tex]BM =ZR[/tex]

[tex]CM =YR[/tex]

So, the measure of the side lengths are:

[tex]YZ =8[/tex]

[tex]BM =15[/tex]

[tex]CM = 11[/tex]

Also, we have the following congruent angles

[tex]\angle B = \angle Z[/tex]

[tex]\angle C = \angle Y[/tex]

[tex]\angle M = \angle R[/tex]

So, the measure of the angles are

[tex]\angle B =45[/tex]

[tex]\angle Y =103[/tex]

The measure of angle M is calculated using:

[tex]\angle M + \angle C + \angle B = 180[/tex]

So, we have:

[tex]\angle M + 103 + 45= 180[/tex]

[tex]\angle M + 148= 180[/tex]

Subtract 148 from both sides

[tex]\angle M = 32[/tex]

Read more about congruent triangles at:

https://brainly.com/question/11329400

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