Answer:
1) x = 25 degrees
2) x = 129 degrees
(3) z = 73 degrees
X = 73 degrees
Y = 107 degrees
(4) 167 degrees
(5) 52 degrees
(6) <1 = 109 degrees
<2 = 71 degrees
(7) <1 = <2 = 86 degrees
(8) <1 = 24 degrees
<2 = 66 degrees
(9) <P = 119 degrees
<Q = 61 degrees
(10) <B = 68 degrees
<C = 22 degrees
Explanation:
(1) x+65 = 90
X = 90- 65
X = 25 degrees
(2) 51+x = 180
X = 180-51
X = 129 degrees
(3) z = 180-107
Z = 73 degrees
X = 73 degrees (vertical angle)
Y = 107 degrees (vertical angle)
(4) 180-13 = 167 degrees
(5) 90-38 = 52 degrees
(6) 5x + 9 + 3x + 11 = 180
8x + 20= 180
8x = 180 - 20
X = 160/8
X = 20
<1 =5(20)+9= 109 degrees
<2 =3(20)+11 = 60+11
<2 = 71 degrees
(7) 17x + 1 = 20x - 14
1+14 = 20x - 17x
15 = 3x
15/3 = x
X = 5
<1 = 17(5)+1 = 86 degrees
<2 = 20(5)-14 = 86 degrees
(8) <1 =3x + 3 and <2 = 10x - 4
3x+3+10x-4 = 90
13x - 1 = 90
13x = 90+1
X = 91/13 = 7
<1 = 3(7)+3=24 degrees
<2 = 10(7)-4 = 66 degrees
(9) <P = 2x-3 and <Q = x
2x - 3 + x = 180
3x = 180 + 3
3x = 183
x = 61
<P = 2(61)-3 = 119 degrees
<Q = 61 degrees
(10) <B = 3x + 2 and <C = x
3x + 2 + x = 90
4x = 90-2
X = 88/4
X = 22
<B = 3(22)+2 = 68 degrees
<C = 22 degrees