Question

Figure PQRS is a parallelogram.

What are the measures of angles P and S?

∠P = 20°; ∠S = 160°
∠P = 40°; ∠S = 140°
∠P = 140°; ∠S = 40°
∠P = 160°; ∠S = 20°

Answer 1

Third choice

i) ∠P = 140°

ii) ∠S = 40°.

Step-by-step explanation:

1) Since the figure is a parallelogram, you know that the angles meet these conditions:

i) ∠P = ∠R = 6x - 10°

ii) ∠Q = ∠S = x + 15°

iii) Condition for a quadrilateral: ∠P + ∠R + ∠Q + ∠S = 360°

2) Now you only need to operate algebraically to solve an equation:

i) replace the valvues in the condition for a quadrilateral:

2 (x + 15) + 2 (6x - 10) = 360

ii) Divide both sides by 2:

x + 15 + 6x - 10 = 180

iii) transpose terms and combine like terms:

7x = 180 - 15 + 10

7x = 175

x = 175 / 7

x = 25°

3) Replace the value of x in each angle:

i) ∠P = ∠R = 6x - 10° = 6 (25) - 10° = 140°

ii) ∠Q = ∠S = x + 15° = 25° + 15° = 40°.

Answer 2

Using the rule of angles in parallel lines, ∠Q and ∠R are supplementary to each other

∠Q+∠R = 180°

`x+15+6x-10=180`

`7x+5=180`

`7x=180-5`

`7x=175`

`x=25`

Size of ∠Q = 25+15 = 40°
Size of ∠R = 6(25) - 10 = 140°

∠Q also supplementary with ∠P, hence ∠P = 140°
∠P supplementary with ∠S, hence ∠S = 40°