Respuesta :

MrGumby
x = 40

This is because STR and STU make up a straight line (180 degrees). Because STR is congruent to SRT, then we know it is 20 degrees, leaving the other 160 degrees for STU. When we divide away the 4, it gives us x = 40. 

It is given that

 ⇒∠SRT≅∠STR

m∠SRT=20°

So,⇒ m∠SRT=m∠STR=20°------{Using (1)]

In ΔSRT

⇒∠SRT+∠RTS+∠TSR=180°-----Angle Sum Property of Triangle

⇒20°+20°+∠TSR=180°

⇒∠TSR=180°-40°

⇒∠TSR=140°

⇒∠STU=∠TRS+∠RST-----[Exterior Angle of triangle is equal to sum of it's two interior opposite Angle]

⇒4x=20°+140°

⇒4x=160°

Dividing both side by 4, we get

x=40°

m∠STU=4×40°=160°

Otras preguntas