Question

state with reason whether or not you can construct Abc in each of the following cases. 1. m<A=45,m<B=60,m<C=75
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Answer 1

Answer:

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Step-by-step explanation:

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

The pairs of adjacent angles are given below:

∠ANB and ∠BNC,

∠BNC and ∠ANC,

∠ANC and ∠ANB,

∠PQR and ∠PQT

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Question 3:

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.

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Question 1:

The measures of some angles are given below. Write the measures of their complementaryangles.

(i) 40° (ii) 63° (iii) 45°(iv) 55° (v) 20° (vi) 90° (vii) x°

ANSWER:

(i)

Let the measure of the complementary angle be a.

40 + a = 90

∴ a = 50°

Hence, the measure of the complement of an angle of measure 40° is 50°

(ii)

Let the measure of the complementary angle be a.

63 + a = 90

∴ a = 27°

Hence, the measure of the complement of an angle of measur