Find the value of x. round to the nearest tenth. !

x ≈ 4.1 cm

Step-by-step explanation:

The segment from the centre to the chord is a perpendicular bisector

The third side of the triangle = 14.6 ÷ 2 = 7.8

We now have a right triangle with legs x and 7.8 with hypotenuse 8.8

Using Pythagoras' identity on the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² + 7.8² = 8.8²

x² + 60.84 = 77.44 ( subtract 60.84 from both sides )

x² = 16.6 ( take the square root of both sides )

x = ≈ 4.1 ( nearest tenth )

4.1

Step-by-step explanation:

⇒The missing side of the triangle is 7.8 cm

We use Pythagoras theorem to solve x

a² = b² + c²

In this case, a = 7.8 cm and c = 8.8 cm

→ 7.8² = x² + 8.8²

( Rearrange )

→ x² = 8.8² - 7.8²

( Simplify )

→ x² = 77.44 - 60.84

( Simplify )

→ x² = 16.6

( Square root )

→ x = 4.074309757

9514 1404 393

  51

Step-by-step explanation:

The exterior angle is equal to the sum of the remote interior angles.

  71° = 20° + x°

  51 = x . . . . . . . . . divide by °, subtract 20

Additional comment

Consider the missing interior angle of the triangle. It is 180° - 71°. It is also 180° -20° -x°. Equating these values and rearranging, we get ...

  71° = 20° + x°

In short, supplements of the same angle are congruent. This relationship can save you the unnecessary work of figuring out the missing interior angle.