extra question of understanding quadrilatrel with answers
please I have to practice
Answers
Answer:
Ok. Here you go.
Step-by-step explanation:
Q.1: A quadrilateral has three acute angles, each measure 80°. What is the measure of the fourth angle?
Solution:
Let x be the measure of the fourth angle of a quadrilateral.
Sum of the four angles of a quadrilateral = 360°
80° + 80° + 80° + x = 360°
x = 360° – (80° + 80° + 80°)
x = 360° – 240°
x = 120°
Hence, the fourth angle is 120°.
Q,2: In a quadrilateral ABCD, the measure of the three angles A, B and C of the quadrilateral is 110°, 70° and 80°, respectively. Find the measure of the fourth angle.
Solution: Let,
∠A = 110°
∠B = 70°
∠C = 80°
∠D = x
We know that the sum of all internal angles of quadrilateral ABCD is 360°.
∠A + ∠B+ ∠C+∠D = 360°
110° + 70° + 80° + x = 360°
260° + x = 360°
x = 360° – 260°
x = 100°
Therefore, the fourth angle is 100°.
Q.3: In a quadrilateral ABCD, ∠D is equal to 150° and ∠A = ∠B = ∠C. Find ∠A, ∠B and ∠C.
Solution: Given,
∠D = 150°
Let ∠A = ∠B = ∠C = x
By angle sum property of quadrilateral,
∠A + ∠B + ∠C + ∠D = 360°
x + x +x+∠D = 360°
3x+∠D = 360°
3x = 360° – ∠D
30 = 360° – 150°
3x = 210°
x = 70°
Hence, ∠A = ∠B = ∠C = 70°.
Q.4: The angles of a quadrilateral are in the ratio of 1 : 2 : 3 : 4. What is the measure of the four angles?
Solution: Given,
The ratio of the angles of quadrilaterals = 1 : 2 : 3 : 4
Let the four angles of the quadrilateral be x, 2x, 3x, and 4x respectively.
The sum of four angles of a quadrilateral is 360°.
Therefore,
x + 2x + 3x + 4x = 360°
10x = 360°
x = 360°/10
x = 36°
Therefore,
First angle = x = 36°
Second angle = 2x = 2 × 36 = 72°
Third angle = 3x = 3 × 36 = 108°
Fourth angle = 4x = 4 × 36 = 144°
Hence, the measure of four angles is 36°, 72°, 108° and 144°.
Q. 5: In quadrilaterals,
(i) which of them have their diagonals bisecting each other?
(ii) which of them have their diagonal perpendicular to each other?
(iii) which of them have equal diagonals?
Solution:
(i) Diagonals bisect each other in:
Parallelogram
Rhombus
Rectangle
Square
Kite
(ii) Diagonals are perpendicular in:
Rhombus
Square
Kite
(iii) Diagonals are equal to each other in:
Rectangle
Square
Q. 6: Adjacent sides of a rectangle are in the ratio 5 : 12, if the perimeter of the rectangle is 34 cm, find the length of the diagonal.
Solution:
Given,
Ratio of the adjacent sides of the rectangle = 5 : 12
Let 5x and 12x be the two adjacent sides.
We know that the sum of all sides of a rectangle is equal to its perimeter.
Thus,
5x + 12x + 5x + 12x = 34 cm (given)
34x = 34
x = 34/34
x = 1 cm
Therefore, the adjacent sides are 5 cm and 12 cm respectively.
i.e. l = 12 cm, b = 5 cm
Length of the diagonal = √(l2 + b2)
= √(122 + 52)
= √(144 + 25)
= √169
= 13 cm
Hence, the length of the diagonal is 13 cm.
Q. 7: The opposite angles of a parallelogram are (3x + 5)° and (61 – x)°. Find the measure of four angles.
Solution:
Given,
(3x + 5)° and (61 – x)° are the opposite angles of a parallelogram.
We know that the opposite angles of a parallelogram are equal.
Therefore,
(3x + 5)° = (61 – x)°
3x + x = 61° – 5°
4x = 56°
x = 56°/4
x = 14°
⇒ 3x + 5 = 3(14) + 5 = 42 + 5 = 47
61 – x = 61 – 14 = 47
The measure of angles adjacent to the given angles = 180° – 47° = 133°
Hence, the measure of four angles of the parallelogram are 47°, 133°, 47°, and 133°.
hope it helps
typed and solved by me as i'm also in grade 8