Question

Find x in the following figure. (Not to scale). Give reasons

Answer 1

Answer: 140°, 50°

Step-by-step explanation:

Left picture:

There are 4 sides so the sum of the angles will be 360°.  Three angles are given: 90°, 60°, and 70° (their total is 220°).  The fourth angle (x) is 360° - 220° = 140°

Right Picture:

There are 5 sides so the sum of the angles will be 540°. Two of the angles are given: 90° and 90°.  Two of the angles form a linear pair.  Their supplementary angles are: 60° and 70°, so those angles are 120° and 110°

Now, you have four of the five angles: 90°, 90°, 120°, and 110° (their total is 410). The fifth angle (linear pair of x) is 540° - 410° = 130°

The fifth angle is a supplement to x: 180° - 130° = 50°