Question

Please help i need answer and explanation.

Answer 1

Answer:

a) ∠TVZ= 95°

Step-by-step explanation:

3a) ∠STY= ∠QTV (vert. opp. ∠s)

3x°= 120°

x°= 120° ÷3

x°= 40

∠TVZ= ∠RVW (vert. opp. ∠s)

∠TVZ= (2x +15)°

∠TVZ= [2(40) +15]°

∠TVZ= (80 +15)°

∠TVZ= 95°

b) Since ∠TVZ and ∠WVZ lies on a straight line,

∠TVZ +∠WVZ= 180° (adj. ∠s on a str. line) -----(1)

∠WVZ= (2x +5)°

∠WVZ= [2(40) +5]°

∠WVZ= (80 +5)°

∠WVZ= 85°

Substitute ∠WVZ= 85° into (1):

∠TVZ +85°= 180°

∠TVZ= 180° -85°

∠TVZ= 95°

Thus, ∠TVZ is indeed 95°.

Notes:

• What is vert. opp. ∠s?

It is an abbreviation used for a property of angles, vertically opposite angles. When two lines intersect each other, the angles facing each other (or the angles on the opposite side of each other) are equal.

• What is adj. ∠s on a str. line?

It is an abbreviation for 'adjacent angles on a straight line'. The sum of all the angles on a straight line is 180°.