Question

What is the measure of angle SPQ in this rhombus? Angle SPR is equal to 2x+15 and angle QPR is equal to 3x-5

Answer 1

Given the rhombus as shown, the indicated angles are;

`\begin{gathered} \angle SPR=2x+15 \\ \angle QPR=3x-5 \end{gathered}`

Observe that angles SPR plus QPR equals angle SPQ.

Therefore we would have;

`\begin{gathered} \angle SPQ=\angle SPR+\angle QPR \\ \angle SPQ=2x+15+3x-5 \\ \angle SPQ=5x+10 \end{gathered}`

Angle SPQ = 5x + 10

Note that the line PR is a bisector of angle SPQ, which means angle SPR and angle QOR are both two equal halves. Therefore;

`\begin{gathered} 3x-5=2x+15 \\ \text{Collect all like terms;} \\ 3x-2x=15+5 \\ x=20 \end{gathered}`

Having determined the value of x, we can now substitute this into angle SPQ as follows;

`\begin{gathered} \text{When,} \\ \angle SPQ=5x+10 \\ \angle SPQ=5(20)+10 \\ \angle SPQ=100+10 \\ \angle SPQ=110 \end{gathered}`

ANSWER:

Angle SPQ = 110 degrees