Question

Use the diagram (click the image above) to find the measure of the segment or angle.

1. m 2. m 3. GH =
4. BC =

Answer 1

Explanation:

From the given angles ∠ABC and ∠GHK,

m∠ABC = m∠GHK [Given]

m∠ABC = m∠GHL + m∠KHL [Since, ∠GHL + ∠KHL = ∠GHK]

(6x + 2)° = (5x - 27)° + (3x + 1)°

6x + 2 = 8x - 26

8x - 6x = 28

2x = 28

x = 14

m(BC) = m(HK) [Given]

3z + 6 = 8z - 9

8z - 3z = 6 + 9

5z = 15

z = 3

m(AB) = m(GH)

5y - 8 = 3y

2y = 8

y = 4

m∠ABC = mGHK = (6x + 2)

= 6(14) + 2

= 86°

m(AB) = m(GH) = 3y

= 3(4)

= 12 units

m(BC) = m(HK) = (3z + 6)

= 3(3) + 6

= 15 units

m(∠KHL) = (3x + 1)°

= 3(14) + 1

= 43°