Find the values of x, y and z. Also their respective angle measures in each
problem.
Please help fast
Answers
Step-by-step explanation:
(1) (4z+6)° = 106° [alternative crossponding angle]
z = 25°
x° = 180°- 106° [consecutive interior angle]
= 74°
x° = 2y° (crossponding angle)
74° = 2y°
y° = 37°
(2) 14y-42° = 11y+6°
3y = 48°
y = 16°
(3) 6x+7° = 180° -65°(consecutive interior angle)
6x +7° = 115°
6x = 108°
x = 18°
(y+9) ° +65° = 180°[supplementry angle]
y+9° = 180° -65°
y = 104°
(4) 5y-4° +3y = 180°
8y = 184°
y° = 23°
and 2x+13° = 3y°
2x + 13° = 3×23
2x = 69-13
2x = 56°
x = 28°
I hope this is helpful for you
Given : intersection of lines
To Find : Values of x , y & z
Solution:
Properties of angles formed by transversal line with two parallel lines :
• Corresponding angles are congruent.
• Alternate angles are congruent. ( Interiors & Exterior both )
• Interior angles are supplementary. ( adds up to 180°)
top left
106° and 2y are linear pair
=> 106° + 2y = 180°
=> 2y = 74°
=> y = 37°
x & 2y are corresponding angles
=> x = 2(37)
=>x = 74°
x and 4z + 6 are alternate interior angles
=> 74 = 4z + 6
=> 4z = 68
=> z = 17°
top right
14y - 42 = 11y + 6 ( vertically opposite angles)
=> 3y = 48
=> y = 16
bottom left
65° and y+9 are linear pair
y + 9° + 65° = 180°
=> y = 106°
y + 9° = 6x + 7° (alternate interior angles)
=> 106° + 9° = 6x + 7°
=> 108° = 6x
=> x = 18°
bottom right
5y - 4 + 3y = 180°
=> 8y = 184°
=> y = 23°
3y = 2x + 13
=> 3(23) = 2x + 13
=> 56 = 2x
=> x = 28
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