Answer:
9. 149 degrees
10. 2 units
Step-by-step explanation:
9. These two triangles are congruent, which means their corresponding side lengths and angles are are equal.
Here, the angle on the bottom triangle marked x actually corresponds to the angle in the top triangle that is unlabelled. That means if we find the unlabelled angle in the top triangle, we've found x.
All angles of a triangle add up to 180, so we can write: x + 17 + 14 = 180
Solve for x: x = 180 - 17 - 14 = 149 degrees
10. Similar triangles have their corresponding angles the same and their corresponding sides in the same <em>ratio</em>, not the same length this time.
Notice that RP is the long leg of triangle PQR and that AC is the long leg of triangle ABC, which means that they correspond to each other and we can write the ratio: RP / AC = 16 / x.
Notice that QP is the short leg of triangle PQR and that AB is the short leg of triangle ABC, which means that they correspond to each other and we can write the ratio: QP / AB = 8 / 1.
Now we can set these two ratios equal and solve for x:
16/x = 8/1
8x = 16
x = 2 units
