215k views
5 votes
An isosceles trapezoid has a consecutive-sides of length: 10,6,10 and 14. Find the measure of each angle if the trapezoid.

An isosceles trapezoid has a consecutive-sides of length: 10,6,10 and 14. Find the-example-1

1 Answer

1 vote

Answer:

Angle A = Angle D = 69° 30'

Angle B = Angle C = 110° 30'

Explanation:

B ___ C

/ \

/ \

A ________ D

AB and CD are 10

BC is 6

AD is 14

If we divide the trapezoid, we can imagine a line.

B_ F_C

/ | \

/ | \

A ___E____ D

AE = ED = 7 (14/2)

BF = FC = 3

So now, we draw another line from B or C to AE or ED

B_ F_ C

/ | | \

/ | | \

A ___E_ G_ D

EG = GD = 3.5 (7/2)

There is a right triangle now, GCD

GD is 3.5 and CD is 10. To determine angle D, we can apply trigonometric function:

CD is H, and GD is A

cos D = A/H

cos D = 3.5/10 → 0.35

angle D = 69° 30'

By theory, we know that angle D and angle A, are the same so:

Angle D = Angle A = 69° 30'

Angle B = Angle C

We also make a cuadrilateral, which is EFCD.

Angle D is 69° 30', Angle E is 90°, Angle F is also 90°

Sum of angles in cuadrilateral is 360°

360° - 69° 30' - 90° - 90° = Angle C = Angle B

Angle C = Angle B = 110° 30'

Let's confirm the angles in the trapezoid:

69° 30' + 110° 30' + 69° 30' + 110° 30' = 360°

A + B + C + D

User Todd Nemet
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories