(1) Given that:
AOB is a line
- angle AOC = 4x-5°
- angle BOC = x+10°
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:
- The sum of two adjacent angles is 180° then they are called Linear pair.
- The sum it two angles is 90° ,they are called Complementary angles.
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