In order for RECT to be a rectangle, what must the value of x be?

Mathematics

1 answer:

Readme [11.4K]3 years ago

6 0

Answer:

x = 21

Step-by-step explanation:

If RECT is a rectangle, each of its interior angles are right angles, 90°. Since ∠RTC is split into two angles, the sum of the two angles must be 90°. (Angles that add to 90° are called complementary angles).

∠RTC = ∠RTE + ∠ETC Formula for complementary angles

90 = 2x + 6 + 42 Substitute the angles

90 = 2x + 48 Combined like terms to simplify

Now isolate "x" to solve

90 - 48 = 2x + 48 - 48 Subtract 48 from both sides

42 = 2x

42/2 = 2x/2 Divide both sides by 2

x = 21

Therefore x is 21.

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