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]
