Question

Find all the angles of the following figures :​

Answer 1

Answer:

Angle OUP = 38 degrees [vertically opposite angle to angle SOR]

Angle ROQ = 52 degrees [vertically opposite angle to angle TOU]

= Angles around a point = 360 degrees

= 360 - (38 × 2) - (52 × 2)

= 360 - 76 - 104

= 360 - 180

= 180

Angle SOT and angle QOP are also vertically opp. angles therefore 180 ÷ 2

= Angle SOT = 90 degrees

= Angle QOP = 90 degrees

CHECK: sum of all angles around a point equal 360 degrees

= (38 × 2) + (52 × 2) + (90 × 2) = 360