Δ MAL and Δ DLA are right triangles. If Δ MAL ≅ ΔDLA, then side DL is congruent to side MA, and ∠ MAL is congruent to ∠ DLA. Given ∠ M is 30 °, side DL is (2x + 10) cm, side MA is (3x – 2) cm, and side AL is (x + 5) cm, answer the following questions below: What is the measurement of DL?

What is the measurement of AL?

What is the measurement of ∠ DLA?

What is the measurement of ∠ AEL?

DL = 34 cm

AL = 17 cm

∠DLA = 60°

∠ADL = 30°

Step-by-step explanation:

Given:

   DL ≅ MA

⇒ 2x + 10 = 3x - 2

⇒ 2x + 12 = 3x

⇒ 12 = x

Substituting found value of x into expressions for DL and AL:

DL = 2x + 10

     = 2(12) + 10

     = 34 cm

AL = x + 5

    = 12 + 5

    = 17 cm

The only way for ΔMAL to be a right triangle, with MA = 34 cm, AL = 17 cm and ∠M = 30° is if

Given:

Sum of interior angles of a triangle is 180°

⇒ ∠DLA + 30° + 90° = 180°

⇒ ∠DLA + 120° = 180°

⇒ ∠DLA = 60°

As ∠M = ∠D = 30°, then ∠ADL = 30°

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