Answer:
x = 3
Question: Find the value of x.
Step-by-step 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
