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 (2

Question

2 years ago

9

5 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

2 answers:

lara [203] · Answer 1 · 2023-05-05T07:59:15+03:00

lara [203]2 years ago

4 0

Answer:

the answer is b

Step-by-step explanation:

Firlakuza [10] · Answer 2 · 2023-05-05T05:38:41+03:00

Answer:

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