Question

How do I solve for angles 1-5?

Answer 1

Keep in mind that the angles of a triangle add up to 180°. The total angle measurement of a line segment is also 180°. The total angle measurement of a right angle is 90°.

Look at the bottom side of the rectangle. It intersects with two lines to form 3 angles: a 70° angle and two angles θ₁

Take the sum of the three angles and set the sum equal to 180°, then solve for θ₁:

2θ₁ + 70° = 180°

2θ₁ = 110°

θ₁ = 55°

We have two right triangles inscribed in the rectangle. Let's focus on the triangle on the right side. It consists of the angles θ₁, θ₃, and a right angle. Take the sum of the three angles and set the sum equal to 180° then solve for θ₃:

θ₁ + θ₃ + 90° = 180°

55° + θ₃ + 90° = 180°

θ₃ = 35°

The triangle on the left side is just the mirror image of the triangle on the right side. These triangles have the same angle measurements, so we can say right away that θ₄ = 35°

Angles θ₂ & θ₃ and θ₄ & θ₅ make up right angles, which have a total angle measurement of 90°. θ₃ = θ₄ = 35°, therefore we can say that θ₂ = θ₅ = 90° - 35°

θ₂ = θ₅ = 55°