Question

What is the measure of ∠SPQ in this rhombus?
m∠SPR = (2x+13)°
m∠QPR = (3x−12)°

Answer 1

The measure of ∠SPQ in the rhombus PQRS, based on ∠ SPR = (2x+13)°, and ∠ QPR = (3x-12)°, is the sum of the two angles of ∠ SPR and ∠ QPR, which equal the whole or ∠ SPQ, in other words (2x+13)° + (3x-12)°.

Answer 2

In a Rhombus The diagonals bisect the angles.

m∠SPR=m∠QPR

Substituting the given values :

2x+13=3x-12

Subtracting 2x both sides:

13=3x-2x-12

13=x-12

Adding 12 both sides:

x=25.

m∠SPR=2x+13=2(25)+13=50+13=63

m∠SPQ=2∠SPR

m∠SPQ=2m∠SPR

m∠SPQ=2x63=126

m∠SPQ= 126 degrees