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pantera1 [17]
2 years ago
9

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

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
Mathematics
2 answers:
lara [203]2 years ago
4 0

Answer:

the answer is b

Step-by-step explanation:

Firlakuza [10]2 years ago
3 0

Answer:

The value of x is 3 ⇒ 2nd answer

Step-by-step explanation:

<u><em>An exterior angle</em></u> is the angle between one side of a triangle and the

extension of an adjacent side

<u><em>The measure of an exterior angle at any vertex of a triangle equal the </em></u>

<u><em>sum of the measures of the two opposite interior angles</em></u>

- 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 ⇒ <u><em>as the rule above</em></u>

∵ 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

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