What is the value of c?

70
55
110
95

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°

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