3. What is the perimeter of Patrick's figure?
1 answer:
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*see attachement for diagram
Answer:
∠P = 140°; ∠S = 40°
Step-by-step explanation:
The figure given is a parallelogram.
Consecutive angles (adjacent angles) of a parallelogram are supplementary.
Therefore:
(x + 15)° + (6x - 10)° = 180°
Solve for x
x + 15 + 6x - 10 = 180
Add like terms
7x + 5 = 180
7x = 180 - 5
7x = 175
x = 175/7
x = 25
✔️m<P = m<R = 6x - 10 (opposite angles of a parallelogram are congruent)
m<P = 6x - 10
Plug in the value of x
m<P = 6(25) - 10 = 140°
✔️m<S = m<Q = x + 15 (opposite angles of a parallelogram are congruent)
m<S = x + 15 = 25 + 15 = 40°
