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°.