Question

What is the measure of ∠SPQ in this rhombus?

m∠SPR=(4x+11)°

m∠QPR=(5x−4)°

Enter your answer in the box.

Answer 1

Answer: 142

Step-by-step explanation:Let's solve your equation step-by-step.

4x+11=5x−4

Step 1: Subtract 5x from both sides.

4x+11−5x=5x−4−5x

−x+11=−4

Step 2: Subtract 11 from both sides.

−x+11−11=−4−11

−x=−15

Step 3: Divide both sides by -1.

−x

−1

=

−15

−1

x=15

so now

(4(15) + 11) + (5(15) - 4) = 142

Answer 2

m∠SPQ=
`142\°`

Explanation:

we know that

In a Rhombus the diagonals bisect the angles,

so

m∠SPR=m∠QPR

substitute the values

`(4x+11)\°=(5x-4)\°`

solve for x

`5x-4x=11+4`

`x=15\°`

m∠SPQ=m∠SPR+m∠QPR

m∠SPQ=
`(4x+11)\°+(5x-4)\°`

m∠SPQ=
`(9x+7)\°`

m∠SPQ=
`(9*15+7)\°=142\°`