Given △ACP ≅ △LNX, find each missing measure.

9514 1404 393

  XL = 13 cm, m∠L = 29°

  AC = 21 cm, m∠C = 29°

  PC = 13 cm, m∠Y = ??  (there is no angle Y in the figure)

Step-by-step explanation:

The figure on the right shows the triangles are isosceles, with XL = XN. That means also PA = PC. Those side lengths are all the same: 13 cm.

  PA = PC = XL = XN = 13 cm

In the same fashion, ...

  LN = AC = 21 cm

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Of course, the angles have a similar relationship:

  ∠A = ∠C = ∠L = ∠N = 29°

The two base angles in the triangle add to 58°, so the third angle is ...

  180° -58° = 122°

  ∠P =∠X = 122°

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Additional comment

As is often the case in over-specified problems, the numbers shown are not consistent The attached figures show the length LN is actually incorrect for the angle and side specified for triangle ACP, or the angles are incorrect for the side lengths specified. What this means is that the answers you get will depend on how you work the problem. Above, we have taken the given numbers and relationships at face value, even though we know they are incorrect.