Triangle r t s is sitting on a horizontal line. line s r extends through point q to form exterior angle t r q. angle r t s is (25 x) degrees. angle t s r is (57 + x) degrees. exterior angle t r q is (45 x) degrees. find the value of x. x = 2 x = 3 x = 33 x = 52

The value of x is 3 ⇒ 2nd answer

Step-by-step explanation:

An exterior angle is the angle between one side of a triangle and the

extension of an adjacent side

The measure of an exterior angle at any vertex of a triangle equal the

sum of the measures of the two opposite interior angles

- Triangle R T S is sitting on a horizontal line

- Line S R extends through point Q to form exterior angle T R Q

- m∠RTS is (25 x)°, m∠TSR is (57 + x)° , m∠TRQ is (45 x)°

* Lets find the value of x

∵ ∠TRQ is an exterior angle of Δ RTS at the vertex R

∵ The opposite interior angles to vertex R are ∠RTS and ∠TSR

∴ m∠TRQ = m∠RTS + m∠TSR ⇒ as the rule above

∵ m∠TRQ = (45 x)°

∵ m∠RTS = (25 x)°

∵ m∠TSR = (57 + x)°

Substitute these measures in the equation above

∴ 45 x = 25 x + 57 + x

∴ 45 x = 26 x + 57

Subtract 26 x from both sides

∴ 19 x = 57

Divide both sides by 19

∴ x = 3

* The value of x is 3