Since quadrilateral ABCD is a cyclic quadrilateral (opposite angles add up to 180 degrees), we can conclude that angle <T + angle <S = 180 degrees.
Given that angle <T is 101 degrees, we can substitute this value into the equation:
101 + angle <S = 180
Solving for angle <S:
angle <S = 180 - 101
angle <S = 79 degrees
Therefore, the measure of angle <S is 79 degrees.
In the quadrilateral above, if the measure of <T is 101°, what is the measure of <S?
11 answers
Which of the following is a quadrilateral that will always have 4 equal sides and 4 right angles?
A quadrilateral that will always have 4 equal sides and 4 right angles is a square.
In a square, all four sides are equal in length and all four angles are right angles, making it a unique quadrilateral with those properties.
In a square, all four sides are equal in length and all four angles are right angles, making it a unique quadrilateral with those properties.
An unknown quadrilateral has the following angle measures.
90°, 90°, 74°, 106°
Which of the following could be the unknown quadrilateral?
90°, 90°, 74°, 106°
Which of the following could be the unknown quadrilateral?
To identify the type of quadrilateral based on its angle measures, we need to analyze the given angles.
The sum of the interior angles of a quadrilateral is always 360 degrees.
Given angle measures:
90°, 90°, 74°, 106°
Sum of the angles:
90 + 90 + 74 + 106 = 360
Since the sum of the angles is 360 degrees, it confirms that the given angles form a quadrilateral.
Now, let's check for potential quadrilateral types:
1. Square: In a square, all angles are 90 degrees, but the given angle measures do not match the square's requirement.
2. Rectangle: A rectangle has two pairs of equal angles, but in this case, the given angles do not form a rectangle.
3. Parallelogram: A parallelogram has opposite angles equal, but the given angles do not satisfy this condition.
4. Trapezoid: The given angles do not fit the properties of a trapezoid.
Based on the given angle measures, none of the options provided match with the angle measures given (90°, 90°, 74°, 106°).
The sum of the interior angles of a quadrilateral is always 360 degrees.
Given angle measures:
90°, 90°, 74°, 106°
Sum of the angles:
90 + 90 + 74 + 106 = 360
Since the sum of the angles is 360 degrees, it confirms that the given angles form a quadrilateral.
Now, let's check for potential quadrilateral types:
1. Square: In a square, all angles are 90 degrees, but the given angle measures do not match the square's requirement.
2. Rectangle: A rectangle has two pairs of equal angles, but in this case, the given angles do not form a rectangle.
3. Parallelogram: A parallelogram has opposite angles equal, but the given angles do not satisfy this condition.
4. Trapezoid: The given angles do not fit the properties of a trapezoid.
Based on the given angle measures, none of the options provided match with the angle measures given (90°, 90°, 74°, 106°).
Is it square
B.
rectangle
C.
parallelogram
D.
trapezoid
B.
rectangle
C.
parallelogram
D.
trapezoid
Given the angle measures of 90°, 90°, 74°, and 106°, let's analyze the possibilities for each type of quadrilateral:
A. Square: In a square, all angles are 90 degrees and all sides are equal. The given angle measures do not match those of a square, so it is not a square.
B. Rectangle: In a rectangle, opposite angles are equal (each pair of opposite angles is equal). The given angle measures do not show this property, so it is not a rectangle.
C. Parallelogram: A parallelogram has both pairs of opposite angles equal. The angle measures do not show this property, so it is not a parallelogram.
D. Trapezoid: A trapezoid does not have specific angle measurements that define its angles, but one pair of opposite angles may be equal. However, the given angle measures do not even match this property, so it is not a trapezoid.
Based on the angle measures given (90°, 90°, 74°, 106°) and the properties of each type of quadrilateral, none of the options provided (square, rectangle, parallelogram, trapezoid) fits the given angle measures.
A. Square: In a square, all angles are 90 degrees and all sides are equal. The given angle measures do not match those of a square, so it is not a square.
B. Rectangle: In a rectangle, opposite angles are equal (each pair of opposite angles is equal). The given angle measures do not show this property, so it is not a rectangle.
C. Parallelogram: A parallelogram has both pairs of opposite angles equal. The angle measures do not show this property, so it is not a parallelogram.
D. Trapezoid: A trapezoid does not have specific angle measurements that define its angles, but one pair of opposite angles may be equal. However, the given angle measures do not even match this property, so it is not a trapezoid.
Based on the angle measures given (90°, 90°, 74°, 106°) and the properties of each type of quadrilateral, none of the options provided (square, rectangle, parallelogram, trapezoid) fits the given angle measures.
Which of the following is a quadrilateral that always has four equal sides and opposite angles congruent?
A quadrilateral that always has four equal sides and opposite angles congruent is a rhombus.
In a rhombus, all four sides are equal in length, and opposite angles are congruent. This property distinguishes a rhombus from other quadrilaterals.
In a rhombus, all four sides are equal in length, and opposite angles are congruent. This property distinguishes a rhombus from other quadrilaterals.
The diagonals divide each figure into four triangles.
Which of the figures are always divided into four congruent triangles by the diagonals?
Which of the figures are always divided into four congruent triangles by the diagonals?
A square is the figure that is always divided into four congruent triangles by the diagonals.
In a square, the diagonals are congruent and bisect each other at 90-degree angles, forming four congruent right triangles. This property holds true for all squares, making it the quadrilateral that is always divided into four congruent triangles by the diagonals.
In a square, the diagonals are congruent and bisect each other at 90-degree angles, forming four congruent right triangles. This property holds true for all squares, making it the quadrilateral that is always divided into four congruent triangles by the diagonals.
3 answers