Two angles which have same vertex and share a common arm are called adjacent angles.
∠PAQ and ∠QAR are adjacent angles.
Adjacent at a point :
The sum of the sizes of the angles at a point is 360 degree
Adjacent angles on a straight line :
The sum of sizes of the angles on a line is 180 degree. The angles are supplementary.
Problem 1 :
x = _____
m ∡MAT = _____
Solution:
7x - 14 + 2x + 5 = 180°
9x - 9 = 180°
9x = 189
x = 21°
m ∡MAT = 7x - 14
7(21) - 14
= 147 - 14
m ∡MAT = 133
Problem 2 :
x = _____
m ∡PIR = _____
m ∡RIM = _____
Solution:
4x + 24 = 7x + 3 (vertically opposite)
7x - 4x = 24 - 3
3x = 21
x = 7
m∡PIR = 4x + 24
= 4(7) + 24
m ∡PIR = 52°
Now,
∡PIR + ∡RIM = 180° (linear pair)
52° + ∡RIM = 180°
∡RIM = 180 - 52
∡RIM = 128°
Problem 3 :
p = _____
m ∡BNK = _____
Solution:
∡ANB + ∡BNK = 180°
5p - 3 + 7p + 15 = 180°
12p + 12 = 180°
12p = 168°
p = 168/12
p = 14
∡BNK = 7p + 15
= 7(14) + 15
= 98 + 15
∡BNK = 113°
Problem 4 :
Which equation is set up correctly?
A) 2x + 5 + 3x - 8 - 180 B) 2x + 5 + 3x - 8 = 5x - 3
C) 2x + 5 + 3x - 8 = 90 D) 2x + 5 = 3x - 8
Solution:
If the two sides of an angle are opposite extensions of the other and they have common vertices, then they are vertical angles.
Vertical angles are equal.
So,
2x + 5 = 3x - 8
So, option (D) is correct.
Problem 5 :
Which equation is set up correctly?
A) 3x + 8 + 5x - 2 = 180 B) 3x + 8 + 5x - 2 = 8x + 6
C) 3x + 8 + 5x - 2 = 90 D) 10 = 2x
Solution:
If the two sides of an angle are opposite extensions of the other and they have common vertices, then they are vertical angles.
Vertical angles are equal.
So,
3x + 8 = 5x - 2
8 + 2 = 5x - 3x
10 = 2x
So, option (D) is correct.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM