Question

The measure of the interior angles of a quadrilateral are x°, 3x°, 5x°, and 7x°. Find the measures of all the interior angles. ?

Answer 1

`color(blue)(22.5^@, 67.5^@, 112.5^@, 157.5^@)`

Explanation:

All the interior angles of a quadrilateral add to `360^@`

If we view `x^@, 3x^@,5x^@,7x^@` as ratios, then we have:

`1:3:5:7`

Add these:

`1+3+5+7=16`

Divide `360^@` by this sum:

`360/16=22.5^@`

Distribute in the given ratio:

`1xx22.5^@`

`3xx22.5^@=67.5^@`

`5xx22.5^@=112.5^@`

`7xx22.5^@=157.5^@`