Answer:
A) For line <em>l = </em>(2x + 8°) + (5x - 10°) = 180° ....... (i)
For line <em>k</em> = (3x + 42°) + (x + 34°) = 180° ....... (ii)
B) In line <em>l, </em>two angles are = 60° and 120°
In line <em>k, </em>two angles are = 120° and 60°
Step-by-step explanation:
Requirement A
To find the measure of each angle, we have to use equation.
According to the graph, line <em>l </em>and<em> k </em>are parallel, therefore, both are straight angle. We know that a straight angle is equal to 180°. Therefore, line <em>l </em>and<em> k </em>are 180°. As both the line are intersected by line <em>j</em>, the lines are separated by two angles. So, the equation for line <em>l</em> is -
(2x + 8°) + (5x - 10°) = 180° ....... (i)
the equation for line <em>k</em> is -
(3x + 42°) + (x + 34°) = 180° ....... (ii)
Requirement B
For line "<em>l </em>"
By solving the equations, we can measure the angles
(2x + 8°) + (5x - 10°) = 180°
or, 2x + 8° + 5x - 10° = 180°
or, 7x - 2° = 180°
or, 7x = 180° + 2°
or, 7x = 182°
or, x = 182° ÷ 7 [Dividing both the sides by 7]
or, x = 26°
Therefore, 2x + 8° = 2 × 26° + 8° = 52° + 8° = 60°
the other angle is = 5x - 10° = 5 × 26° - 10° = 130° - 10° = 120°
For line "<em>k </em>"
(3x + 42°) + (x + 34°) = 180°
or, 3x + 42° + x + 34° = 180°
or, 4x + 76° = 180°
or, 4x = 180° - 76° [Deducting 76° from the both the sides]
or, 4x = 104°
or, x = 104° ÷ 4
Hence, x = 26°
Therefore, 3x + 42° = 3 × 26° + 42° = 78° + 42° = 120°
The other angle is = x + 34° = 26° + 34° = 60°
