Question

In an adjoining figure, XY|| BC. Find the values of x, y, z.​

Answer 1

Answer:

X=30°

Y=10°

Z=10°

Step-by-step explanation:

WHEN WE SEE THE FIGURE, WE SEE THAT

• Y=Z and,
• X=30°

WHICH IS IN ACCORDANCE WITH CORRESPONDING ANGLE PROPERTY AND

• X+Y=40°

WHICH IS DERIVED FROM "THE SUM OF A TRIANGLE IS EQUAL TO 180°" PROPERTY.

HENCE, BY SEEING THIS WE SOLVE THE EQUATION LIKE THIS:-

$x + y = 40$

AND REPLACING 'X' BY 30° WE SEE,

$30 + y = 40 \\ y = 40 - 30 \\ y = 10$

AND SINCE Y=Z THEREFORE

Z=Y=10°

Answer 2

Answer:

x = 30, y = 110, z = 110

Step-by-step explanation:

In triangle ABC, A + B + C = 180 (angle sum property)

40 + 30 + z = 180

70 + z = 180

z = 180 - 70 = 110

Given that XY II BC, Z + XYC = 180 (co-interior angles)

110 + XYC = 180

XYC = 180 - 110 = 70

XYC + XYA = 180 (straight angle property)

70 + y = 180

y = 180 - 70 = 110

In triangle AXY, A + X + Y = 180 (angle sum property)

40 + x + 110 = 180

x + 150 = 180

x = 180 - 150 = 30