the sides BA DC of quadrilateral ABCD are produced to P Qrespectively angle DAP=b,angle BCQ=a,angle D=y, angle B=x - Maths - Lines and Angles

Question

the sides BA DC of quadrilateral ABCD are produced to P
Qrespectively angle DAP=b,angle BCQ=a,angle D=y, angle B=x showt
that angle x+angle y=angle a+angle b

Manbar Singh · Accepted Answer

GIVEN :ABCD is a quadrilateral, in which ∠QCB = a ; ∠PAD =
b∠ADC = y ; ∠ABC = xTO PROVE :x + y = a + bCONSTRUCTION
:Join BD PROOF :In ∆ABD, we have ∠PAD = ∠ABD +
∠ADB Exterior angle theorem ⇒b = ∠ABD + ∠ADB 1In
∆CBD, we have ∠QCB = ∠CBD + ∠CDB Exterior angle
theorem ⇒a = ∠CBD + ∠CDB 2adding 1 and 2, we get b + a
= ∠ABD + ∠ADB + ∠CBD + ∠CDB⇒a + b = ∠ABD +
∠CBD + ∠ADB + ∠CDB⇒a + b = x + y

the sides BA DC of quadrilateral ABCD are produced to P Qrespectively. angle DAP=b,angle BCQ=a,angle D=y, angle B=x. showt that angle x+angle y=angle a+angle b