Question

8) Find the measure of < SPQ

Answer 1

Check the picture below.

now, ∡SPQ is a bit ambiguous, it could be ∡SRQ or ∡STUQ, anyhow we'll be doing the green one in the picture, ∡STUQ

`86+x+x+60+154~~ = ~~360\implies 2x+300=360\implies 2x=60 \\\\\\ x=\cfrac{60}{2}\implies x=30\hspace{9em}\stackrel{ \measuredangle STUQ }{86+30+30}\implies \text{\LARGE 146}^o`