[3] Answer: ∠DCB = 128°
Explanation:
First, we know a straight angle is equal to 180 degrees.
3x° + 5° + x° + 11° = 180°
4x° + 16° = 180°
4x° = 164°
x° = 41°
Next, we can apply this same knowledge of straight angles to ∠DCA. We will substitute the value of x above into the expression for angle ACB.
180° - (x + 11)° = ∠DCB
180° - (41 + 11)° = ∠DCB
180° - 52° = ∠DCB
128° = ∠DCB
[4] Answer: ∠DEC = 126°, ∠BEC = 54°
Explanation:
We will also apply the knowledge of straight angles being equal to 180 degrees here.
5x° + 36° + 3x° = 180°
8x° + 36° = 180°
8x° = 144°
x° = 18°
Next, we will substitute this value of x back into the expressions for each angle.
5x° + 36° 3x°
5(18)° + 36° 3(18)°
126° 54°
Lastly, we know that vertical angles are congruent.
∠AEB = ∠DEC = 126°
∠AED = ∠BEC = 54°