Question

this is the figure
Question: If ABCD is a rectangle with angle ABD = 40°, then find the value of x, y, and z​

Answer 1

consider the point of intersection as O.

now, AO=OB

we know equal sides in a ∆ form opp. equal angles .

therefore,

40° =angle OAB

now,

$x + oab = 90 \\ x = 90 - 40 = 50$

in ∆ ADC by ∆ law,

$x + z = 90 \\ 50 + z = 90 \\ z = 90 - 50 = 40$

In ∆OAB, by ∆law,

$y + 40 + oab = 180 \\ y = 180 - 40 - 40 \\ y = 100$

hope it helps you