Question

What is the value of v?

angle 1: 31°
angle 2: 16v–4°
angle 3: 15v+34°

Answer 1

Answer:

8

Step-by-step explanation:

To solve the question, we can use the exterior angle theorem.

The exterior angle theorem states that, In a triangle, the exterior angle (angle formed outside the triangle by extending one of its sides) is equal to the sum of the two interior angles.

Here, angle 1 (31°), angle 2(16v - 4)° are the interior angles and angle 3 (15v + 34°) is the exterior angle

So, angle 1 + angle 2 = angle 3

$31 + 16v - 4 = 15v + 35$

Solving for v,

$27 + 16v = 15v + 35$

Subtract 15v from both sides,

$27 + 16v - 15v = 35$

$27 + v = 35$

subtract 27 from both sides,

$v = 35 - 27$

$v = 8  $

Therefore, the required value of v is 8.