**Given information:**

- Two angles of the quadrilateral measure 70 degrees each.
- The other two angles are in a ratio of 5:6.

**Let's solve step by step:**

**Step 1: Determine the sum of all angles in a quadrilateral:**
- A quadrilateral has a total of four angles.
- The sum of all angles in a quadrilateral is always 360 degrees.

**Step 2: Find the measure of the two known angles:**
- Two angles of the quadrilateral measure 70 degrees each.
- So, the sum of these two angles is 70 + 70 = 140 degrees.

**Step 3: Find the remaining angles:**
- The other two angles are in a ratio of 5:6.
- Let's assume the ratio is 5x and 6x.
- The sum of these two angles will be 5x + 6x = 11x.

**Step 4: Set up an equation:**
- The sum of all angles in a quadrilateral is 360 degrees.
- So, we can write the equation as:
140 + 11x = 360

**Step 5: Solve the equation:**
- Subtract 140 from both sides of the equation:
11x = 360 - 140
11x = 220

- Divide both sides of the equation by 11:
x = 220 / 11
x = 20

**Step 6: Calculate the measure of the remaining angles:**
- Substitute the value of x in the ratio 5x and 6x:
First angle: 5x = 5 * 20 = 100 degrees
Second angle: 6x = 6 * 20 = 120 degrees

**Step 7: Verify the solution:**
- Sum of all four angles: 70 + 70 + 100 + 120 = 360 degrees (which is the total sum of angles in a quadrilateral)
- Therefore, the solution is verified.

**Answer:**
The measure of each angle in the quadrilateral is as follows:
- Two angles measure 70 degrees each.
- The other two angles measure 100 degrees and 120 degrees, respectively.

1 st angle =70 degree
2nd angle =70 degree
3rd angle = 100 degree
4th angle = 120 degree.