Question

Pl.z si.r hel.p m.e math geometry questio.n......

x=65
y=60
p=60
q=65
r=115 How?​

Answer 1

`\\ \rm{:}\dashrightarrow p+120=180`

`\\ \rm{:}\dashrightarrow p=60`

And

• q=65°(Opposite angles are equal

Now

`\\ \rm{:}\dashrightarrow r+65=180`

`\\ \rm{:}\dashrightarrow r=115`

So

`\\ \rm{:}\dashrightarrow x=q(Opposite interior angles)=65`

• y=p=60°

Answer 2

p = 60°

r = 115°

q = 65°

y = 60°

x = 65°

Explanation:

Linear pair: a pair of adjacent angles formed when two lines intersect. The two angles are always supplementary and so their measures sum to 180°.

Therefore, the linear pairs are:

p + 120° = 180°

⇒ p = 60°

r + 65° = 180°

⇒ r = 115°

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Vertical angle theorem: a pair of opposite angles formed by intersecting lines. Vertical angles are always congruent (equal).

Therefore, the vertical angles are q and 65°:

⇒ q = 65°

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Consecutive interior angle theorem: if a transversal intersects two parallel lines, each pair of consecutive interior angles is supplementary and so their measures sum to 180°.

Therefore, the consecutive interiors angles are:

120° + y = 180°

⇒ y = 60°

x + r = 180°

⇒ x + 115° = 180°

⇒ x = 65°