Question

find the measure of all angles in the figure given below ​

Answer 1

Answer:

∠LOP = 87°

∠POM = 93°

Step-by-step explanation:

From the figure,

∠LOP + ∠POM = 180° (As LM is a straight angle = 180°)

∠LOP = 4a + 3°

∠POM = 5a - 12°

Substituting values of ∠LOP and ∠POM,

(4a + 3°) + ( 5a - 12°) = 180°

4a + 3° + 5a - 12° = 180°

4a + 5a + 3°- 12° = 180°

9a - 9° = 180° (adding the a's and adding the numbers)

9a = 180° + 9° (taking -9° from LHS to RHS)

9a = 189°

a = 189°/9 (Dividing both sides by 9)

a = 21°

Now, substituting values of a = 21° as obtained, in the equations above:

⇒ ∠LOP = 4a + 3° = (4 × 21°) + 3° = 84° + 3° = 87°

⇒ ∠POM = 5a - 12° = (5 × 21°) - 12° = 105° - 12° = 93°

Hope it helps :D

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Answer 2

Answer:

∠POM = 93°

∠POL = 87°

Step-by-step explanation:

=> (5a-12)° + (4a+3)° = 180° [Since LM is a line, and thus a Linear Pair is formed]

=> 5a-12+4a+3 = 180 [Brackets opened]

=> 9a-9 = 180 [Added like terms]

=> 9a = 180+9 [Transposition]

=> 9a = 189

=> a = 189/9 [Again, Transposition]

=> a = 21

Now, substitute the value of a

∠POM = (5a-12)° = 5(21)-12 = 105-12 = 93°

∠POL = (4a+3)° = 4(21)+3 = 76+3 = 87°

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