Answer:
The value of x is 18
The value of y is 6
Step-by-step explanation:
- If two angles in a triangle are equal in measures, then the sides opposite to them are equal in length
- If the three angles of a triangle are equal in measures, then the three sides of the triangle are equal in lengths
- In a triangle, the measure of an exterior angle at a vertex of the triangle equals the sum of the measures of the two opposite interior angles to this vertex.
→ In Δ TRS
∵ ∠RTS and ∠RST have the same mark
∴ m∠RTS = m∠RST
∵ RT and RS are the opposite sides to ∠RTS and ∠RST
→ By using the first rule above
∴ RT = RS
∵ RS = 11
∴ RT = 11
→ In Δ RUT
∵ ∠RUT, ∠RTU, and ∠TRU have the same mark
∴ m∠RUT= m∠RTU = m∠TRU
→ By using the second rule above
∴ RU = UT = RT
∵ RT = 11
∴ UT = 11
∵ UT = x - 7
→ Equate the right sides of UT
∴ x - 7 = 11
→ Add 7 to both sides
∴ x - 7 + 7 = 11 + 7
∴ x = 18
∴ The value of x is 18
∵ The sum of the measures of the interior angles of a Δ is 180°
→ That means the measure of each angle is 180° ÷ 3 = 60°
∴ m∠RUT= m∠RTU = m∠TRU = 60°
∵ ∠URT is an exterior angle of Δ TRS
∵ ∠RTS and ∠RST are the opposite interior angles of ∠URT
→ By using the third rule above
∴ m∠RTS + m∠RST = 60°
∵ m∠RTS = 5y°
∴ m∠RTS = m∠RST = 5y
→ Substitute them in the rule above
∴ 5y + 5y = 60
∴ 10y = 60
→ Divide both sides by 10
∴ y = 6
∴ The value of y is 6
