Question

In the given figure, ↔AB || ↔CD. The transversal ↔PQ intersects ↔AB at point X and ↔CD at Y respectively. If ∠XYC = 85°, find the measure of the remaining angles.

Answer 1

SOLUTION:-
GIVEN BY:- AB||CD
here,
∠XYC = 85°,
WE GET,
∠XYC and ∠XYD both are supplementary angle
we know that sum of supplementary angle = 180.
●∠XYD = 180-85° = 95
∠XYD and ∠PXB both are corresponding angel
●∠XYD = ∠PXB = 95
∠PXB and ∠AXY both are vertically opposite angles.
●∠PXB = ∠AXY = 95
similarly
∠XYD = ∠CYQ = 95
∠XYC = ∠DYQ = 85
∠XYC = ∠AXP = 85

■I HOPE ITS HELP■

Answer 2

Hello,

Solution:

Total angles formed are 8.

→ Pair of corresponding angles :

(i) ∠ AXP and ∠ CYX = 85°

Now,∠AYX + ∠XYD = 180°

∠XYD = 180°-∠AYX

∠XYD = 95°

So,

(ii) ∠BXP and ∠DYX = 95°

Now,

∠AXP +∠AXY =180°

∠AXY= 180°-∠AXP = 180°-85° = 95°

So, both ∠AXY and ∠QYC = 95° ; corresponding angle pair

By this way ∠YXB and ∠QYD = 85°

Hope it helps you.