Question

A quadrilateral has two angles that measure 295° and 35°. The other two angles are in a ratio of 7:8. What are the measures of those two angles?

° and
°

Answer 1

To find the measures of the remaining angles in the quadrilateral, we first need to know the sum of all angles in a quadrilateral. The sum of the angles in any quadrilateral is 360°.

We know two angles:
- Angle 1: 295°
- Angle 2: 35°

Let's add these two angles together:
\[
295° + 35° = 330°
\]

Next, we can find the sum of the remaining two angles by subtracting their sum from 360°:
\[
360° - 330° = 30°
\]

So, the sum of the two remaining angles, which we'll call \(x\) and \(y\), is:
\[
x + y = 30°
\]

We also know that the two angles are in a ratio of 7:8. This means we can express them as:
\[
x = 7k \quad \text{and} \quad y = 8k
\]
for some value \(k\).

Now we can substitute \(x\) and \(y\) into the equation:
\[
7k + 8k = 30°
\]
\[
15k = 30°
\]

Now, solve for \(k\):
\[
k = \frac{30°}{15} = 2°
\]

Now we can find the measures of the angles \(x\) and \(y\):
\[
x = 7k = 7 \cdot 2° = 14°
\]
\[
y = 8k = 8 \cdot 2° = 16°
\]

Thus, the measures of the two angles are:
\[
x = 14° \quad \text{and} \quad y = 16°
\]

To summarize:
The measures of the other two angles are **14°** and **16°**.