contestada

PERSEVERE The Flatiron Building in New York City is one of America's oldest skyscrapers, completed in 1902. Its floor plan is approximately a
right triangle. As shown in the figure, 5th Avenue is perpendicular to East 22nd Street, and m 2B is 10 less than 3 times mLC.

a. find the angle measures in the floor plan ( measure of A, B, and C )

b. find measure of BCD in two ways. explain each method in simple terms.

PERSEVERE The Flatiron Building in New York City is one of Americas oldest skyscrapers completed in 1902 Its floor plan is approximately a right triangle As sho class=

Respuesta :

sqdancefan

Answer:

  a. (A, B, C) = (90°, 65°, 25°)

  b. BCD = 155°

Step-by-step explanation:

The interior acute angles of the right triangle can be found by writing an equation representing the relation between them. The exterior angle can be found using the relations between exterior angles and interior angles.

__

a.

Angle A is given as a right angle, so measures 90°. Let C represent the measure of angle C in degrees. Then angle B has measure 3C-10. Those two angles are complementary, so ...

  C +(3C-10) = 90

  4C = 100

  C = 25

  B = 3(25) -10 = 65

The angle measures are ...

  • A = 90°
  • B = 65°
  • C = 25°

__

b.

Angle BCD is the exterior angle adjacent to interior angle C. As such, it is supplementary to angle C:

  BCD = 180° -C = 180° -25° = 155°

An exterior angle is equal to the sum of the remote interior angles. That means ...

  BCD = A +B = 90° +65° = 155°

_____

Additional comment

An exterior angle is equal to the sum of the remote interior angles, because both the exterior angle and the sum of the remote interior angles are supplementary to the adjacent interior angle. Angles supplementary to the same angle have the same measure.

Otras preguntas