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
