Question

What is the measure of ∠SPQ in this rhombus?


m∠SPR=(4x+11)°

m∠QPR=(5x−4)°

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°

Answer 1

ok so all you have to do is set SPR and QPR equal like this
4x+11=5x-4
and solve to get x=15
then substitute in 15 for x in both equations
4(15)+11 and 5(15)-4
both =71 and add them up to get SPQ=142.

Answer 2

Using the angle property of a rhombus, the measure of the m∠SPQ is 142°

• m∠SPR = (4x + 11)°

• m∠QPR = (5x - 4)°

Since the diagonal bisects the vertex angles of a rhombus ; m∠SPR = m∠QPR

Hence we can equate the values of the two angles to obtain the value of x :

4x + 11 = 5x - 4

Collect like terms

4x - 5x = - 4 - 11

-x = - 15

x = 15°

Therefore, the value of x = 15°

m∠SPR = (4(15) + 11)° = 60 + 11 = 71°

m∠SPQ = m∠SPR + m∠QPR = 142°

Hence, the measure of m∠SPR is 142°

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