Question

answer these two i will mark u as brainlist

Answer 1

$\sf\huge\mathbb{ANSWER:}$

SOLUTION : 1

Given :

m||n

∠1:∠2=3:2

To find :

Measure of All angles from ∠1 to ∠8

Solution :

∠1:∠2=3:2

Let∠1 be 3x

& ∠2 be 2x

As we can see than ∠1 and ∠2 lie on same line with common arm, they form linear pair.

Linear Pair

∠1+∠2=180°

3x+2x=180°

5x=180°

x=180°/5

x=36°

Hence, ∠1=3x=3×36°=108°

& ∠2=2×36°=72°

m||n & l as transversal line

Corresponding angles are equal

∠1=∠6=108°

∠2=∠5=108°

Alternate (interior+exterior) angles are equal

∠6=∠3=108°

∠5=∠4=72°

∠2=∠7=72°

∠1=∠8=108°

Hence, measures of all angles are :

$\bf\red{∠1=108°, ∠2=72°}$

$\bf\red{∠3=108°, ∠4=72°}$

$\bf\red{∠5=72°, ∠6=108°}$

$\bf\red{∠7=72°, ∠8=108°}$

SOLUTION : 2

Given :

L||m

t and u are transversal lines

To find :

measure of angles a, b, c, d

Construction :

Consider ∠1 as shown in figure .

Solution :

When L|| m & t is transversal line

→d=65° [corresponding angles]

→b=d=65° [alternate interior angles]

When L||m and u is transversal line

→a=120° [Vertically opposite angles]

→a= ∠1=120° [Alterate interior angles]

→∠1+c=180° [Linear pair]

120°+c=180°

c=180°-120°

c=60°

$\bf\red{a=120°, b=65°}$

$\bf\red{c=60°, d=65°}$