Given That ∠TOS Is A Right Angle With Ray OP At The Middle Of The Angle, ∠TOS Is Th…

Given that ∠TOS is a right angle with ray OP at the middle of the angle, ∠TOS is the sum of two angles ∠TOP and ∠POS and ∠TOP ≅ ∠POS, find the value of a, if m∠TOP = 2a + 9

A.18

B.19

C.21

D.20

Answer:

A. 18

Step-by-step explanation:

2a + 9 = 45° ( I got 45 since 90 ÷ 2 is 45°)

2a = 45 -9

2a = 36

a = 18

[tex] \large\underline \bold{{QUESTION}}[/tex]

Given that ∠TOS is a right angle with ray OP at the middle of the angle, ∠TOS is the sum of two angles ∠TOP and ∠POS and ∠TOP ≅ ∠POS, find the value of a, if m∠TOP = 2a + 9

[tex] \large\underline \bold{{SOLUTION}}[/tex]

[tex]\textsf{∠TOP ≅ ∠POS}[/tex]

[tex]\textsf{ 2a+9 ≅ 2a+9}[/tex]

[tex]\textsf{It states that their sum if 90°.}[/tex][tex]\textsf{It follows that:}[/tex]

  • [tex]\sf{∠TOP + ∠POS = 90°}[/tex]
  • [tex]\sf{(2a+9)+(2a+9) = 90°}[/tex]
  • [tex]\sf{4a+18=90°}[/tex]
  • [tex]\sf{4a = 90°-18}[/tex]
  • [tex]\sf{4a = 72°}[/tex]
  • [tex]\sf{a = 72÷4}[/tex]
  • [tex]\boxed{\sf{a = 18}}[/tex]

[tex] \large\underline{ \bold{ANSWER}}[/tex]

  • OPTION A (18)

#[tex]\sf{10_2}[/tex]

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