181,133 views
10 votes
10 votes
Find the measured of the numbered angles in the rectangle. Geometry Chapter 7.4

Find the measured of the numbered angles in the rectangle. Geometry Chapter 7.4-example-1
User Oodini
by
2.8k points

1 Answer

12 votes
12 votes

Answer:

∠3 = 18°

∠4 = 144°

∠2 = 36°

∠1 = 72°

Explanation:

From the concept of alternate interior angles,

∠3 = 18°

Since the diagonal divides the rectangle into 4 parts with 2 of the rectangles being similar.

Then, the triangle with ∠3 & ∠4 is an Isosceles triangle and as such;

∠4 = 180 - 2(∠3)

∠4 = 180 - 2(18)

∠4 = 180 - 36

∠4 = 144°

∠2 = 180 - ∠4 (because sum of angles on a straight line is 180°)

∠2 = 180 - 144

∠2 = 36°

Like it was done for angle ∠4 above;

∠1 = (180 - 36)/2

∠1 = 144/2

∠1 = 72°

User Rob Rolnick
by
2.7k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.