Question

What is true about the angles in the diagram shown below? A D E (31) The value of x is B C Enter the correct answers in the boxes.​

Answer 1

x = 22.5

∠ADE = 67.5

Explanation:

The sum of interior angles in a triangle is equal to 180° and the given is a right triangle so we can find the value of x easily:

90 + x + 3x = 180 add like terms

90 + 4x = 180 subtract 90 from both sides

4x = 90 divide both sides by 4

x = 22.5

To find the measure of angle ADE we use the same equation:

90 + 22.5 + ∠ADE = 180 add like terms

112.5 + ∠ADE = 180 subtract 112.5 from both sides

∠ADE = 67.5