Question

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.

Answer 1

x = 3

Question: Find the value of x.

Explanation:

Given:

- 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

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

19 x = 57

x = 3