Question

answer this please ​

Answer 1

Step-by-step explanation:

This is the answer

Answer 2

Step-by-step explanation:

Given :-

PQ||RS,∠PAC = 70°,∠ACS = 100°

To find :-

Determine ∠ABC , ∠ BAC and ∠ CAQ

Solution :-

Given that

PQ || RS

∠ PAC = 70°

∠ACS = 100°

Let ∠ABC = x°

Let ∠BAC = y°

In ∆ ABC , BC is extended to CS

=>∠ACS is the exterior angle

We know that

An exterior angle formed by extending any side of a triangle is equal to the sum of opposite interior angles.

The opposite interior angles of ∠ACS are ∠ABC and ∠BAC

=>∠ACS =∠ABC +∠BAC

=> 100° = x°+y°

x° + y° = 100° ------------(1)

and

PQ || RS and AB is the transversal then

Alternative interior angles are equal.

=>∠ABC =∠PAB

=> x° = 70°

x° = 70° --------(2)

On Substituting the value of x in (1) then

=> 70°+y° = 100°

=> y° = 100°-70°

=> y°=30°

So, We have

x° = 70°

=>∠ABC = 70°

and

y° = 30°

=>∠BAC = 30°

and

∠ACS+ ∠ACB = 180°

since they are linear pair

=> 100° +∠ACB = 180°

=>∠ACB = 180°-100°

=>∠ACB = 80°

PQ || RS and AC is the transversal then

Alternative interior angles are equal.

=>∠ACB =∠CAQ

=> 80° = ∠CAQ

=> ∠CAQ = 80°

Answer :-

∠ABC = 70°

∠ACB = 80°

∠BAC = 30°

∠CAQ = 80°

Used formulae:-

• An exterior angle formed by extending any side of a triangle is equal to the sum of opposite interior angles.

• If two parallel lines intersecting by a transversal then the alternative interior angles are equal.