Copy the problem, mark the givens in the diagram, and write a Statement/Reason proof. Given: MN ≅ MA ME ≅ MR Prove: ∠E ≅ ∠R

Step-by-step explanation:

Given: MN ≅ MA

          ME ≅ MR

Prove: ∠E ≅ ∠R

From the given diagram,

YN ≅ YA

EY ≅ RY

<EMA = <RMN (right angle property)

EA = EY + YA (addition property of a line)

NR = YN + RY (addition property of a line)

EA ≅ NR (congruent property)

ΔEMA ≅ ΔRMN (Side-Side-Side, SSS, congruence property)

<MNR ≅ MAE (angle property of congruent triangles)

Therefore,

<E ≅ <R (angle property of congruent triangles)

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°