Two angles of a quadrilateral measure 178° and 78°. The other two angles are in a ratio of 6:7. What are the measures of those two angles?
Let the other two angles be 6x and 7x. The sum of all four angles in a quadrilateral is 360°, so we can set up an equation:
178° + 78° + 6x + 7x = 360°
Simplifying and solving for x, we get:
261° + 13x = 360°
13x = 99°
x = 7.6° (rounded to one decimal place)
Now we can find the measures of the other two angles:
6x = 6(7.6) = 45.6°
7x = 7(7.6) = 53.2°
Therefore, the measures of the other two angles are 45.6° and 53.2°.
To find the measures of the other two angles of the quadrilateral, we can use the fact that the sum of the angles of a quadrilateral is always 360 degrees.
Step 1: Find the sum of the two known angles
The sum of the two known angles is 178° + 78° = 256°.
Step 2: Find the sum of the other two angles
Let the two unknown angles be 6x and 7x, where x is a common factor.
The sum of the other two angles is 6x + 7x = 13x.
Step 3: Set up an equation
Since the sum of all four angles is 360°, we can write the equation:
256° + 13x = 360°.
Step 4: Solve the equation
Subtract 256° from both sides of the equation:
13x = 360° - 256° = 104°.
Divide both sides of the equation by 13:
x = 104° / 13 = 8°.
Step 5: Find the measures of the two unknown angles
Substitute x = 8° into the expression for the angles:
6x = 6 * 8° = 48°.
7x = 7 * 8° = 56°.
Therefore, the measures of the other two angles are 48° and 56°.