Question

Use the diagram below to explain why the three statements are true.

1) s+t=180
2) u=p+s
3) t+u+v=360

Answer 1

See below.

Explanation:

1) s + t = 180

Angles s and t are supplementary since they are a linear pair.

2) p + s + r = 180 (sum of measures of interior angles of triangle)

u + r = 180 (supplementary since they are a linear pair)

Solve second equation above for r.

r = 180 - u

Substitute 180 - u for r in first equation above.

p + s + 180 - u = 180

p + s = u

u = p + s

3) t + u + v = 360

r + u = 180 (linear pair)

s + t = 180 (linear pair)

p + v = 180 (linear pair)

Add the three equations:

r + u + s + t + p + v = 540

Rearrange the left side.

(p + r + s) + (t + u + v) = 540

p + r + s = 180 (sum of measures of interior angles of triangle)

180 + t + u + v = 540

Subtract 180 from both sides.

t + u + v = 360