Question

What is the measure of angle D?
(Geometry) with details and steps!!!​

Answer 1

32°

Explanation:

If you look at the figure there are two distinct triangles formed by the intersection of the two lines

These are ΔAEB and ΔCED

Consider ΔAEB

Two of its angle measure are given:
m∠EAB = 14° and m∠EBA = 45°

The measure of the third angle ∠AEB can be computed from the fact that the sum of the three angles of a triangle add up to 180°

So we get the equation:
14 + 45 + m∠AEB = 180

59 + m∠AEB = 180

m∠AEB = 180 -59 = 121°

We also have
m∠AEB = m∠CED
since they are vertically opposite angles formed at intersection E by the two straight lines AD and BC

So m∠CED = 121°

Now considering the triangle ΔCED we have two angles known to us
m∠ECD = 27° and m∠CED = 59°

The sum of the measures of the three angles ∠ECD, ∠CED and ∠CDE must add up to 180°

==> 27 + 121 + ∠CDE = 180

148 + ∠CDE = 180

∠CDE = 180 - 148 = 32°

So ∠D measures 32°

Answer 2

See below

Explanation:

The angle at E in the UPPER triangle

is 180 - -45 -14 = 121° ( because the angles of any triangle sum to 180 °)

The angle below this is the same value 121°

then 27 + 121 + D = 180 shows D = 32°