Question

According to the figure given here,

(i) what is the sum of BÔC and CÔD ?
(ii) what is the complement of BÔC ?
(iii) what is the magnitude of AÔD ?
(iv) what is the sum of AÔD and DÔE?
(v) what is the supplement of DÔE ?
(vi) what is the complement of DÔE ?​

Answer 1

#1

• <BOC+<COD=25+65=90

#2

Let the complement be x

• x=90-25=75

#3

• <AOD=20+25+65=110

#4

• <AoD+<DOE=110+70=180°

#5

• x=90-70=20

Answer 2

(i) 90°

(ii) CÔD

(iii) AÔD = 110°

(iv) 180°

(v) AÔD

(vi) AÔB

Explanation:

Two angles are said to be complementary if they add up to 90°.

Complementary angles can either be adjacent or non-adjacent.

Two Angles are said to be supplementary if they add up to 180°.

Complementary angles can either be adjacent or non-adjacent.

(i) BÔC + CÔD = 25 + 65 = 90°

(ii) BÔC = 25°

Therefore the complementary angle measures 90 - 25 = 65°

So the complement of BÔC is CÔD

(iii) AÔD = 20 + 25 + 65 = 110°

(iv) AÔD + DÔE = 110 + 70 = 180°

(v) DÔE = 70°

Therefore the supplementary angle measures 180 - 70 = 110°

So the supplement of DÔE is AÔD

(vi) DÔE = 70°

Therefore the complementary angle measures 90 - 70 = 20°

So the complement of DÔE is AÔB