Answer:
23) 57° 24) 85° 25) 60 and 120° 26) 70° and 110°
Step-by-step explanation:
23) The unknown angle is 57°(a corresponding angle.
The given angle is corresponding to ye unknown angle
24. The unknown angle is 85°. The given angle is equal to the unknown angle becuaee both angle are alternate i.e they lie in alternate sides of each other
25) sum of angles on a straight line is 180°
Since the angles 7x+11 and 17x+1 both lies on the same straight line, the sum of the Two angles will be 180°.
Mathematically,
7x+11 + 17x+1 = 180°
24x + 12 = 180°
24x = 180-12
24x = 168°
x = 168/24
x = 7°
The angle 7x+11 = 7(7)+11
= 49+11
= 60°
The other angle will be 180-60 = 120°
26) First, the x+77 is equal to the angle adjacent to x+117. This makes both angle lies adjacent to each other and on the same straight line.
Note that sum of angles on a straight line is 180°
Since the angles x+77 and x+117 both now lies on the same straight line, the sum of the Two angles will be 180°.
x+77+x+117 = 180
2x + 194 = 180
2x = 180-194
2x = -14
x = -7°
Angle x+77 will give -7+77 = 70° and angles x+117 will give -7+117 = 110°
The angles are 70° and 110°
