1. If the given figure, AOB is a straight line. Find the value of (i) x
(ii)∠AOC
(iii) ∠BOC
2. The complement of 65° is _.

(1) Given that:

AOB is a line

From the figure,

angle AOC and angle BOC are linear pair

They are supplementary.

⇛angle AOC + angle BOC = 180°

⇛4x-5° + x+10° = 180°

⇛(4x+x) +(-5°+10°) = 180°

⇛5x+5° = 180°

⇛5x = 180°-5°

⇛5x = 175°

⇛x = 175°÷5 = 175°/5

Therefore, x = 35°

(i) The value of x = 35°

(ii) angle AOC = 4x-5°

⇛4(35°)-5°

⇛140°-5°

⇛135°

(iii) angle BOC = x+10°

⇛35°+10°

⇛45°

(2) Given that

The angle = 65°

We know that

The complementary angle of x° is 90°-x°

The complementary angle of 65°

⇛90°-65°

⇛25°

Additional comment:

also read similar questions: m∠AOC is a straight angle angle BOC = 6x + 29 m∠BOC=6x+29 angle AOB = 3x + 124 m∠AOB=3x+124 ∘ Find angle BOC

Point B is in the interior of ∠AOC, m∠AOC = 108°, m∠AOB = 3m∠BOC. Find m∠AOB.