triangle ABD abd BDC have common side BD angle ABD =x Angle DBC=y Angle BCD=z, AB || DC If - Maths - Triangles

Question

triangle ABD abd BDC have common side BD angle ABD =x Angle
DBC=y Angle BCD=z, AB || DC If x =4/3y
and y =3/8z, find the values of x, y and z

Pronay · Accepted Answer

$∠ ABD= x$

Given: $AB ∥ DC$

$x = \frac{4}{3} y y = \frac{3}{8} z$

$AB ∥ DC \Rightarrow ∠ BDC= ∠ ABD= x (alternate angles)$

In ΔBDC

$x + y + z = 180^{\circ} \Rightarrow \frac{4}{3} y + y + z = 180^{\circ} \Rightarrow \frac{7}{3} y + z = 180^{\circ} \Rightarrow \frac{7}{3} \times \frac{3}{8} z + z = 180^{\circ} \Rightarrow \frac{7}{8} z + z = 180^{\circ} \Rightarrow z = \frac{180 \times 8}{15} \Rightarrow z = 96^{\circ}$

$y = \frac{3}{8} z = \frac{3}{8} \times 96 = 36^{\circ}$

$x = \frac{4}{3} \times y = \frac{4}{3} \times 36 = 48^{\circ}$

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triangle ABD abd BDC have common side BD.angle ABD =x Angle DBC=y Angle BCD=z, AB || DC. If x =4/3y and y =3/8z, find the values of x, y and z.

triangle ABD abd BDC have common side BD.angle ABD =x Angle DBC=y Angle BCD=z, AB || DC. If x =4/3y

and y =3/8z, find the values of x, y and z.