Very confused with this

∠ D = 28°

Step-by-step explanation:

The external angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ EBC is an exterior angle of Δ ABE, thus

∠ EBC = 90° + 34° = 124°

BD bisects ∠ EBC, so

∠ EBD = 124° ÷ 2 = 62° , then

∠ D = 180° - (90 + 62)° = 180° - 152° = 28° ( angle sum of triangle )

4

Step-by-step explanation:

To find:

The remainder, when 3^0 + 3^1 + 3^2 + ... +3^2009 is divided by 8

Approach and Working:

Rem (3^0/8) = 1

Rem (3^1/8) = 3

Rem (3^2/8) = 1

Rem (3^3/8) = 3

Rem (3^4/8) = 1

Rem (3^5/8) = 3 and so on…

We can observe that,

For even powers of 3, the remainder is 1

And for odd powers of 3, the remainder is 3.

Therefore, we can rewrite the given series, in terms of its remainders, as

= 1 + 3 + 1 + 3 + 1 + 3 + … + 3 = 1005 pairs of (1 + 3) = 1005 x 4 = 4020

Rem (4020/8) = 4