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°