MATH SOLVE

4 months ago

Q:
# 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

Accepted Solution

A:

Answer:The value of x is 3 ⇒ 2nd answerStep-by-step explanation:An exterior angle is the angle between one side of a triangle and the extension of an adjacent sideThe 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 + 57Subtract 26 x from both sides∴ 19 x = 57 Divide both sides by 19∴ x = 3* The value of x is 3