Question

(a) In GIVEN FIGURE, a = b = c, name the angle which is congruent to ∠AOC (b) If m∠ AOD is 75° then what will be the measure of ∠AOB? (c)Is it correct to say that any two right angles are congruent? Give reasons to justify your answer (3M) (write answer on foolscap paper)​

Answer 1

Answer:

Are the following pairs adjacent angles? If not, state the reason.

(i) ∠PMQ and ∠RMQ (ii) ∠RMQ and ∠SMR

(iii) ∠RMS and ∠RMT (iv) ∠SMT and ∠RMS

ANSWER:

Two angles which have a common vertex, a common arm and separate interiors are said to be adjacent angles

(i)

In ∠PMQ and ∠RMQ, M is the common vertex and MQ is the common arm.

Therefore, ∠PMQ and ∠RMQ are adjacent angles.

(ii)

The angles ∠RMQ and ∠SMR have a common vertex M, but don't have common arm.

Therefore, ∠RMQ and ∠SMR are not adjacent angles.

(iii)

The angles ∠RMS and ∠RMT have a common vertex M, but don't have common arm.

Therefore, ∠RMS and ∠RMT are not adjacent angles.

(iv)

In ∠SMT and ∠RMS, M is the common vertex and SM is the common arm.

Therefore, ∠SMT and ∠RMS are adjacent angles.