Question

Select all the true statements(select all that apply)

A.m∠MLN = 120
B.m∠QLP = 50
C. m∠NLO + m∠OLP = m∠NLP
D. m∠QLP + m∠PLO = m∠MLN + m∠NLO
E.m∠QLO − m∠QLP = m∠MLO − m∠MLN

Answer 1

B.m∠QLP = 50

C. m∠NLO + m∠OLP = m∠NLP

D. m∠QLP + m∠PLO = m∠MLN + m∠NLO

Explanation :

B. In this the protractor reads 50° so it's correct!

C. In this when the two angels are taken together it's NLP

D. So in this the addition of the 1st two(QLP and PLO) angels =90° as shown in the protractor just as the addition of the next 2 (MLN and NLO)

Answer 2

B.m∠QLP = 50

C. m∠NLO + m∠OLP = m∠NLP

D. m∠QLP + m∠PLO = m∠MLN + m∠NLO

Explanation:

∵ In the compass, the angle from the terminal side to clockwise direction is estimated by the above scale and the angle from the terminal side to anticlockwise direction is estimated by the below scale,

Thus, by the given compass,

m∠MLN = 60°,

m∠MLO = 90°,

m∠QLO = 90°,

m∠QLP = 50°

∠NLP can be divided into angles ∠NLO and m∠OLP,

⇒ m∠NLO + m∠OLP = m∠NLP

Now, ∠MLN and ∠NLO are linear pairs,

⇒ m∠MLN + m∠NLO = 180°,

Similarly,

∠QLP and ∠PLO are linear pairs,

⇒ m∠QLP + m∠PLO = 180°,

⇒ m∠MLN + m∠NLO = m∠QLP + m∠PLO

∠MLN and ∠NLO parts of angle ∠MLO,

⇒ m∠MLN + m∠NLO = m∠MLO,

⇒ m∠NLO = m∠MLO - m∠MLN

Similarly,

∠OLP and ∠QLP parts of angle ∠QLO

⇒ m∠OLP + m∠QLP = m∠QLO,

⇒ m∠OLP = m∠QLO - m∠QLP

But, m∠NLO ≠ m∠OLP

⇒ m∠QLO − m∠QLP ≠ m∠MLO − m∠MLN