Question

Test revision for a test tomorrow --

The explanation is more important than the answer. As far as I know, here is the most relevant formula :

Sum of interior angles in a regular polygon :
180 x ( n - 2 ) ( n represents the number of sides )

Thank you!

Answer 1

• 
  `46°`

Given:

• ∠CAB = 38°
• ∠BCA = 96°

To find :

• ∠ADE

Solution :

We are given a triangle with another triangle formed inside of it making one side of both triangles parallel to each other

In order to find the size of angle ADE, we firstly are required to know what a pair of parallel lines is.

• A pair of parallel lines consists of two lines that extend in the same direction but never meets .

Moreover,

• When a pair of parallel lines get intersected by any other line (a transversal), their corresponding angles become congruent to each other.

Thus,

In the case of ΔADE and ΔABC where BC II DE, angle ABC becomes congruent to angle ADE and so does angle ABC to angle AED.

Now,

getting back to the question asked, we will find the size of angle ADE by working out the measure of angle ABC that is given by the sum of angle CAB and angle BCA subtracted from the sum of interior angles in a traingle i.e. 180° ( 180° (3-2) = 180°)

• ∠ABC = 180° - (∠CAB + ∠BCA)
• ∠ABC = 180° - (38° + 96°)
• ∠ABC = 180° - 134°
• ∠ABC = 46°

Since, ∠ABC = ∠ADE ( corresponding angles of ll lines ), hence,

• ∠ADE = 46°

Therefore, the size of angle ADE is 46°.