Exercise 119 Page 625

From the exercise we know that the triangles are congruent. Therefore, they must have the same size and shape, which means they have three pairs of congruent angles and three pairs of congruent sides. The unknown side in the left triangle must therefore be $5$ units, and the unknown side in the right triangle must be $7$ units.

When we have identified corresponding sides, we can also identify corresponding angles.

Finally, using the Triangle Angle Sum Theorem we can determine the triangle's last angle.

m ∠ θ + 8 5^{\circ} + 5 0^{\circ} = 18 0^{\circ} \Leftrightarrow m ∠ θ = 4 5^{\circ}

Now we can complete the triangle.