Question

Please help me with this.

Answer 1

1. 55°
2. 75°
3. 55°
4. 15°

Explanation:

You want the measures of the numbered angles in the figure comprised of overlapping right triangles.

Complementary angles

The acute angles in a right triangle are complementary, as are the two angles into which a right angle is divided.

∠1 +35° = 90° ⇒ ∠1 = 55°

∠3 +35° = 90° ⇒ ∠3 = 55°

Exterior angle

The angle marked 70° is exterior to the bottom right triangle, so is equal to the sum of angles 3 and 4.

∠3 +∠4 = 70°

55° +∠4 = 70° ⇒ ∠4 = 15°

Angle 2 is the other acute angle in the bottom right triangle, so ...

∠2 = 90° -∠4 = 90° -15°

∠2 = 75°