The correct answer is A. 70°
Step-by-step explanation:
1. Let's review the information given to us for solving the question:
∠ A = 100°
∠ B = 95°
∠ C = ?
∠ D = ?
2. What is the value of ∠ C ?
For solving this question and finding the value of ∠ C, we draw a bisector line that starts on angle ∠ A to angle ∠ C, that divides these two angles into two equal parts ( ∠ A₁, ∠ A₂) and (∠ C₁, ∠ C₂) dividing the quadrilateral into two triangles : Δ ABC and Δ ACD.
After drawing that bisector line we will know two interior angles of the Δ ABC, this way:
∠ A₁ = Original ∠ A ( 100°), divided in two equal angles ( ∠ A₁, ∠ A₂) is 50°
∠ B = 95°
∠ C₁ = x
Now, we can found the value of angle ∠ C₁ (one of the equal parts of angle ∠ C, after drawing the bisector line)
The three interior angles in a triangle will always add up to 180°, so we can calculate:
∠ A₁ + ∠ B + ∠ C₁ = 180
Replacing with the real values:
50 + 95 + ∠ C₁ = 180
∠ C₁ = 180 - 95 - 50
∠ C₁ = 180 - 145
∠ C₁ = 35 ⇒ ∠ C₂ = 35 (Two equal parts after drawing the bisector line)
So, ∠ C = 70°
3. What is the value of ∠ D ?
The four interior angles in any quadrilateral will always add up to 360°, so we can calculate:
∠ A + ∠ B + ∠ C + ∠ D = 360
Replacing with the real values:
100 + 95 + 70 + ∠ D = 360
∠ D = 360 - 100 - 95 -70
∠ D = 95°
