Anonymous
Anonymous asked in Science & MathematicsMathematics · 3 weeks ago

# What steps would be involved in solving a question like this one ?

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• geezer
Lv 7
3 weeks ago

The two triangles DBE and DCE share the same base length .. DE.

So ...

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.

Therefore ...

If angle at C is 38 degrees then angle at B is 76 degrees.

Now ...

The sum of the angles of a triangle are always 180 degrees.

So ..

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.

• David
Lv 7
3 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'

• Anonymous
3 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.)

• 3 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°