Answer to Question #132877 in Geometry for Emma Donaldson

Question

Find m∠RSQ and m∠TSQ. S T Q R (8x + 18)° (15x − 43)

RSQ= __° 

TSQ= __°

Answer 1

they add to 90$\degree$ so

∠TSQ + ∠RSQ = 90$\degree$

(15x - 43)$\degree$ + (8x + 18)$\degree$ = 90$\degree$

add like terms

23x$\degree$ - 25$\degree$ = 90$\degree$

add 25 to bothn sides

23x$\degree$ = 115$\degree$

divide both sides by 23$\degree$

$\frac{23x\degree}{23\degree}$ = $\frac{115\degree}{23\degree}$

x = 5$\degree$

NOW ∠RSQ = (8x + 18)$\degree$

= {8(5) + 18}$\degree$

= ( 40 + 18 )$\degree$

∠RSQ = 58$\degree$

the other angle is just

90$\degree$ - ∠RSQ = ∠TSQ

90$\degree$ - 58$\degree$ = ∠TSQ

32$\degree$ = ∠TSQ

SO, ∠TSQ = 32$\degree$

∠RSQ = 58$\degree$