Question

Figure PQRS is a parallelogram.

Parallelogram P Q R S is shown. Angle Q is (x + 15) degrees and angle R is (6 x minus 10) degrees.

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

Answer: The measures of angles P and S cannot be determined without the value of x.

Step-by-step explanation:

Since a parallelogram has opposite angles that are congruent, we can determine the measures of angles P and S based on the given angles Q and R.

Angle P is opposite angle Q, so ∠P = ∠Q = (x + 15) degrees.

Angle S is opposite angle R, so ∠S = ∠R = (6x - 10) degrees.

Answer 2

C) ∠P = 140°; ∠S = 40°

Explanation:

If PQRS is a parallelogram, angle Q is adjacent to angle R.

As adjacent angles of a parallelogram sum to 180°, set the sum of angle Q and angle R to 180°, and solve for x:

⇒ ∠Q + ∠R = 180°

⇒ (x + 15)° + (6x - 10)° = 180°

⇒ x + 15 + 6x - 10 = 180

⇒ 7x + 5 = 180

⇒ 7x = 175

⇒ x = 25

Substitute the found value of x into the expressions for angle Q and angle R:

⇒ ∠Q = (x + 15)°

⇒ ∠Q = (25 + 15)°

⇒ ∠Q = 40°

⇒ ∠R = (6x - 10)°

⇒ ∠R = (6(25) - 10)°

⇒ ∠R = (150 - 10)°

⇒ ∠R = 140°

The opposite angles of a parallelogram are equal.

Angle P is opposite angle R, so ∠P = 140°.

Angle Q is opposite angle S, so ∠S = 40°.