Question
A quadrilateral has two angles that measure \( 247^{\circ} \) and \( 51^{\circ} \). The other two angles are in a ratio of \( 11: 20 \). What are the measures of those two angles? \( \square^{\circ} \) and
Ask by Elliott Welch. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The other two angles are 22° and 40°.
Solution
In any quadrilateral, the sum of the interior angles is 360°. Two of the angles are given as 247° and 51°. First, calculate the sum of the remaining two angles:
Total of given angles = 247° + 51° = 298°
Sum of the remaining two angles = 360° - 298° = 62°
Let the other two angles be represented as 11x and 20x, according to the ratio 11:20. Then:
11x + 20x = 31x = 62°
Now, solve for x:
x = 62° / 31 = 2°
Now, determine the measures of the two remaining angles:
Angle 1 = 11x = 11 × 2° = 22°
Angle 2 = 20x = 20 × 2° = 40°
Thus, the measures of the other two angles are 22° and 40°.
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Bonus Knowledge
The sum of the angles in any quadrilateral is always \( 360^{\circ} \). Here, we add the given angles: \( 247^{\circ} + 51^{\circ} = 298^{\circ} \). Now, subtract this from \( 360^{\circ} \) to find the sum of the other two angles: \( 360^{\circ} - 298^{\circ} = 62^{\circ} \). Let the measures of the two unknown angles be \( 11x \) and \( 20x \) based on the given ratio. The equation is \( 11x + 20x = 62^{\circ} \), which simplifies to \( 31x = 62^{\circ} \). Solving for \( x \) gives \( x = 2 \). Thus, the angles are \( 11x = 22^{\circ} \) and \( 20x = 40^{\circ} \). The measures of the two angles are \( 22^{\circ} \) and \( 40^{\circ} \).
