Question

In the figure, if m (arc DXE) = 100° and m (arc AYC) = 40°, find ∠DBE. ​

Answer 1

ye lo appka answer........

Answer 2

The value of ∠DBE will be 30°

Step-by-step explanation:

Given:

m(arc DXE)= 100°

m(arc AYC)= 40°

To find:

value of ∠DBE

Construction:

Draw ∠DAE such that it intercepts arc DXE

Draw ∠AEC such that it intercepts arc AYC

Note: Refer to the figure below for better understanding

Solution:

In the figure,

∠ DAE and ∠AEB are the inscribed angles...............(construction)

∴ By inscribed angle theorem

∠DAE= $\frac{1}{2}$ m(arc DXE) and ∠AEB= $\frac{1}{2}$ m(arc AYC)

∠DAE= $\frac{1}{2}$ m(arc DXE)

∴ ∠DAE=  $\frac{1}{2}$ (100°).................(given)

∴ ∠DAE= 50°...........(1)

∠AEB= $\frac{1}{2}$ m(arc AYC)

∴ ∠AEB= $\frac{1}{2}$ (40°)..................(given)

∴ ∠AEB=20°..........(2)

Consider ΔABE,

∠AEB=20°........(from 2)

∠DAE is the exterior angle for ΔABE

∴ ∠DAE = ∠AEB+∠DBE..............(by exterior angle theorem)

∴ 50°= 20°+∠DBE...........[from (1) & (2)]

∴ 50°- 20°= ∠DBE

∴∠DBE= 30°

Thus the measure of ∠DBE will be 30°