x = 55° vertically opposite angles
y+ 55° = 180°
y = 180°- 55°
y = 125°
z = 125°

Yes, because the sum of two right angles is 180° and form a linear pair.

No, the sum of the measures of two obtuse angles is more than 180°.

Yes, In the figure
∠AOB and ∠BOC are adjacent angles.
Also ∠AOB + ∠BOC = 180°
∴ ∠AOB and ∠BOC are supplementary

Let the angles be x and y.
From the given information y = 3x - 42^o
x = y (Corresponding angles are equal)
x = 3x - 42^o
2x = 42^o
x = 21^o
The corresponding angles is 21^o

From the figure
<1 + x^o = 180^o
108 + x^o = 180^o
x = 72^o
<2 + y^o = 180^o
123 + y^o = 180^o
y = 57^o
Also we know that
72 + 57 + 0
129 + 0

Since Alternate interior angles are equal
<G = <H
Given that <G + <H = 180^o
<G + <G = 180. (...<G = <H)
2 <G = l80^o
ie., <G = 90^o and <H = 90^o

The two real - life situations where we use parallel lines are
(i) Railway tracks
(ii) Edges of a door frame

Sum of angles at a point = 360°
∴ x + 2x + 3x + 4x + 5x = 360°
15x = 360°
x = \(\frac{360°}{15}\)
x = 24^o
From the given angles the largest angle is 5x
= 5 x 24° = 120°
The largest angle is 120°.

Let x be the all five angles. The sum of all six angles at a point is 360^o.
x + x + x+ x + x + 45 = 360^o
45^o + 5x  = 360°
5x = 360^o - 45
5x^o = 315°
x^o = \(\frac{{315}^o}{15}\)
x^o = 63°
∴ Measure of all 5 equal angles = 63°.

Let the three angles be x, 4x and 7x .
The sum of three angles at a points is supplementary
∴ x + 4x + 7x = 360°
12x = 360°
x^o = \(\frac{{360}^o}{12}\)
x = 30°
If x = 30^o then
4x = 4 x 30° = 120°
7x = 7 x 30° = 210°.
∴ The three angles are 30°, 120° and 210°.

From the figure
∴ ∠JlL = ∠JIK + ∠KIL
= 38° + 27°
= 65°
∴ ∠JlL = 65°

From the figure the pair ofadjacent angles are
i) \(\angle\)ABG and, \(\angle\)CBG
ii) \(\angle\) DCE and \(\angle\)ECF
iii) \(\angle\)ECE and \(\angle\)ACF
iv) \(\angle\)ACF and \(\angle\)ECD.
v) \(\angle\)BCF and \(\angle\)FCE

(i) The angles 1 and 2 are exterior angles
(ii) The apgles 1 and 2 are Alternate exterior angles
(iii) The angles 1 and 2 are corresponding angles
(iv) The angles 1 and 2 are interior angles
(v) The angles 1 and 2 are alternate interior angles
(vi) The angles 1 and 2 are coruesponding angles

(i) From the figure
∠AOC + ∠BOC = 180°
72° + x^o = 180°
72° + x^o - 72° = 180° - 72°
x^o = 108°
(ii) From the figure
∠AOC + ∠BOC = 180°
3x + 42° - 180°
3x^o + 42° - 42°= 180^o - 42°
3x^o = 138°
x^o = \(\frac{{138}^o}{3}\) = 46^o
x^o = 46°
(iii) From the figure
∠AOC + ∠BOC = 180°
4x^o + 2x^o = 180°
6x^o = 180°
x^o = \(\frac{{138}^o}{6}\)
x^o = 30°