What steps would be involved in solving a question like this one ?
- geezerLv 73 weeks ago
The two triangles DBE and DCE share the same base length .. DE.
If DBE has it's 'peak' at the centre of the circle
and DCE has it's 'peak' at the circumference of the circle (above the 'peak' at B)
then the angle at B will be twice the angle at C.
If angle at C is 38 degrees then angle at B is 76 degrees.
The sum of the angles of a triangle are always 180 degrees.
180 - 76 will tell you 'the sum of the angle at D and the angle at E'.
180 - 76 = 104
and because we know that the angle at D and the angle at E are the same
104/2 = 52 degrees ... the angle at E
Which is a .. the angle you are looking for.
- DavidLv 73 weeks ago
Angle 'a' is part of an isosceles triangle with two equal sides and two equal base angles whereas angle B is twice angle angle C making it 76 degrees.
There are 180 degrees in a triangle and so 180 - 76 = 104 and 104/2 = 52 degrees which is the size of angle 'a'
- Anonymous3 weeks ago
The angle at the centre is twice that at the circumference, so DBE = 76.
(Theorem The angle subtended by an arc at the centre is twice the angle subtended at the circumference.)
Then deduct that from 180 to get the remaining angles of triangle BDE = 104
(Sum of angles in a triangle = 180)
As it is an isoceles triangle these are equal, so alpha is 52 deg
(Isoceles triangle theorem: If two sides of a triangle are congruent, then angles opposite those sides are congruent.)
- 冷眼旁觀Lv 63 weeks ago
DBE is an isosceles Δ, and thus the two base angles are equal.
∠BDE = ∠BED = α
In ΔDBE, Sum of interior angles:
∠DBE + ∠BDE + ∠BED = 180°
76° + 2α = 180°
2α = 104°
α = 52°