Answer:
5) 106°
6)
7) 46°
8) 102°
Explanation:
Find the measure of the angle indicated in bold.
We are to find x
5) This follows the rule of Alternate Interior angles
= 12x + 10 = 13x + 2
Collect like terms
= 10 - 2 = 13x - 12x
= 8 = x
x = 8
The angle indicated in bold = (13x + 2)°
= 13 × 8 + 2
= 104 + 2
= 106°
6) This follows the rules of consecutive interior angles
x - 70 + 130 + x = 180
2x + 60 = 180
2x = 180 - 60
2x = 120
x = 120/2
x = 60
7)This follows the rule of Alternate Interior angles
22x + 2 = 21x + 6
Collect like terms
22x - 21x = 6 - 2
x = 4
The angle in bold is (22x + 2)°
Hence,
(22 × 2 + 2)°
44 + 2 = 46°
The measure of the angle is 46°
8) This follows the rule of corresponding angles
13x + 11 = 14x + 4
Collect like terms
11 - 4 = 14x - 13x
7 = x
x = 7
The angle in bold is (14x + 4) °
(14 × 7 + 4)°
=( 98 + 4)°
= 102°