Answer:
a) 8°
b) 155°
c) 25°
d) 155°
Explanation:
The angle of a straight line is 180°, so
5x-15+20x-5 = 180
25x-20=180
25x= 200
x= 8
LAT = 20x-5 = 20(8)-5 = 155°
TAO= 3x+1= 3 (8)+1= 25°
LAP= 5(8)-15 =25°
The angle at a point equals 360° so
LAP+ PAO+TAO+LAT= 360°
25+PAO+ 25+ 155=360°
PAO= 360- 205
PAO= 155°
There's another way to get the answer of d.
The vertically opposite angles are equal when two lines intersect each other, so
PAO=LAT=155°
Hope this helps, have a great day!