The value of x in ∆ABC is 3 feet and the value of x in ∆XYZ is 4 feet.
How the values of x were calculated in the triangles.
5)Given ∆ABC and ∆PQR
angleA ≅ angleQ( both measure 87⁰)
angleC ≅ angleD( both measure 40⁰)
AC ≅ PR(equal sides)
Therefore,
∆ABC ≅ ∆PQR(Angle-Side-Angle ASA)
Their corresponding sides are equal in length
AB corresponds to PQ,
AB = PQ
x + 4 = 7
x = 7-4
= 3 feet
6) From ∆DEF and ∆XYZ
angleD ≅ angleX( both measure 23⁰)
angleE ≅ angleY( both measure 64⁰)
DF ≅ XZ(equal sides)
Therefore,
∆DEF ≅ ∆XYZ(Angle-Side-Angle ASA)
Their corresponding sides are equal in length
DE corresponds to XY,
DE = XY
15 = 4x - 1
4x = 15+1
4x = 16
x = 16/4
= 4 feet
The value of x in ∆ABC is 3 feet and the value of x in ∆XYZ is 4 feet.