Find the values of x and y in the diagram.

The value of x is 18

The value of y is 6

Step-by-step explanation:

→ 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

idk

step-by-step explanation:

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