Can anybody help me with trying to figure out how to do this?

a. Angle A  = 35

As triangle ABD has angle ADB equal to 90°

=> ABD is the right triangle

=> Angle ABD + Angel A = 90°

=> Angel A = 90° - Angel ABD = 90°- 55° = 35°

So Angel A = 35°

b. Angle CBD = 61

As triangle BDC has angle BDC equal to 90°

=> BDC is the right triangle

=> Angle CBD + Angel C = 90°

=> Angel CBD = 90° - Angel C = 90°- 29° = 61°

So Angel CBD = 61°

c. AD = 32.77

As ABD is the right triangle, so that we have the formula:

sin (an angel) = opposite side/ hypotenuse

=> sin angel ABD = AD/ AB

=> AD = sin angel ABD x AB = sin 55° x 40 ≈ 32.77

So AD = 32.77

d. BC = 47.32

As ABD is the right triangle, according to Pythagoras theorem, we have:

=> BD ≈ 22.94

As BCD is the right triangle, so that we have the formula:

sin (an angel) = opposite side/ hypotenuse

=> sin angel C = BD/ BC

=> BC = BD/ sin angel C = 22.94 / sin 29° ≈ 47.32

So BC = 47.32

e.  CD = 41.39

As BCD is the right triangle, according to Pythagoras theorem, we have:

=> CD ≈ 41.39

f. BD = 22. 94 (part d)

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d

step-by-step explanation:

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°