Respuesta :

CHERLYNnotCHERRY

Answer:

Question 21

  • ∠PQS = 22°
  • ∠PQR = 44°

Question 22

  • ∠ABC = 47°
  • ∠CBD = 47°

Question 23

  • ∠ABD = 35°
  • ∠DBC = 35°
  • ∠ABC = 70°

Step-by-step explanation:

When the question says a line bisects an angle which means that this line is cut exactly at the centre of an angle so both angles will be the same :

Question 21,

[tex]∠PQR = ∠SQR[/tex]

[tex]∠PQS = 22°[/tex]

[tex]∠PQR = ∠PQS + ∠SQR[/tex]

[tex]∠PQR = 22 + 22 = 44°[/tex]

Question 22,

[tex]∠ABD = 94°[/tex]

[tex]∠ABC = ∠CBD = 94 \div 2 = 47°[/tex]

Question 23,

[tex]∠ABD = ∠DBC[/tex]

[tex]x + 15 = 4x - 45[/tex]

[tex]4x - x = 15 + 45[/tex]

[tex]3x = 60[/tex]

[tex]x = 60 ÷ 3 = 20°[/tex]

[tex]∠ABD = 20 + 15 = 35°[/tex]

[tex]∠DBC = 4(20) - 45 = 35°[/tex]

[tex]∠ABC = ∠ABD + ∠DBC = 35 + 35 = 70°[/tex]