In this triangle (not drawn to scale) the angle at A is twice that
at B, while the angle at B is 16° more than that at C.
What is the value of the angle at A ?

Let's call the angles at vertices \( A \), \( B \), and \( C \) as \( \angle A \), \( \angle B \), and \( \angle C \), respectively.

### Step 1: Express relations between the angles.
From the problem:
- \( \angle A = 2 \times \angle B \)  (Angle at \( A \) is twice that of \( B \)).
- \( \angle B = \angle C + 16^\circ \)  (Angle at \( B \) is 16° more than that at \( C \)).

### Step 2: Set up the equation for the sum of the angles.
In any triangle, the sum of the interior angles is always \( 180^\circ \):
\[
\angle A + \angle B + \angle C = 180^\circ
\]

### Step 3: Substitute the relations into the sum equation.
We already have \( \angle A = 2 \times \angle B \) and \( \angle B = \angle C + 16^\circ \). We can substitute \( \angle C \) as \( \angle B - 16^\circ \) into the equation.

Now, substituting into the sum of angles:
\[
2 \times \angle B + \angle B + (\angle B - 16^\circ) = 180^\circ
\]

### Step 4: Simplify the equation.
\[
2\angle B + \angle B + \angle B - 16^\circ = 180^\circ
\]
\[
4\angle B - 16^\circ = 180^\circ
\]
\[
4\angle B = 196^\circ
\]
\[
\angle B = \frac{196^\circ}{4} = 49^\circ
\]

### Step 5: Calculate \( \angle A \).
Now that we know \( \angle B = 49^\circ \), we can calculate \( \angle A \):
\[
\angle A = 2 \times \angle B = 2 \times 49^\circ = 98^\circ
\]

### Step 6: Calculate \( \angle C \).
Using \( \angle B = \angle C + 16^\circ \), we find:
\[
\angle C = \angle B - 16^\circ = 49^\circ - 16^\circ = 33^\circ
\]

Thus, the angles in the triangle are:
- \( \angle A = 98^\circ \)
- \( \angle B = 49^\circ \)
- \( \angle C = 33^\circ \)

The value of \( \angle A \) is **98°**.

Would you like further details or have any questions? 

Here are five related questions:
1. How do you solve for the angles of an isosceles triangle?
2. What is the sum of the interior angles in a quadrilateral?
3. Can you prove why the sum of angles in any triangle is 180°?
4. How does the exterior angle theorem apply in triangles?
5. What is the difference between an acute and obtuse triangle?

**Tip:** Remember, the sum of the interior angles of any polygon is \((n - 2) \times 180^\circ\), where \(n\) is the number of sides.

In this triangle (not drawn to scale) the angle at A is twice that at B, while the angle at B is 16° more than that at C. What is the value of the angle at A?

Learn how to calculate the angle at vertex A in a triangle where the angle at A is twice that of B, and B is 16° more than C. This detailed solution involves using triangle angle sum properties and basic algebra. Suitable for students in Grades 6-8.

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