Question

If PQRS is a rectangle,

find the measure of ZQPT.
P
(16x - 17)
(10x + 1)°
T
R
S

Answer 1

∠ QPT = 59°

Explanation:

• the opposite sides are parallel

then

∠ SPT = ∠ QRT ( alternate angles ), that is

16x - 17 = 10x + 1 ( subtract 10x from both sides )

6x - 17 = 1 ( add 17 to both sides )

6x = 18 ( divide both sides by 6 )

x = 3

then

∠ SPT = 16x - 17 = 16(3) - 17 = 48 - 17 = 31°

• the vertices of a rectangle are right

∠ QPS = 90° , so

∠ QPT = 90° - ∠ SPT = 90° - 31° = 59°