find the value of x in 2+ 3x degrees + 62 degrees is a complementary and is equal to 90degrees in chapter lines and angles
Answers
Answer:
Classify each of them on the basis of the following.
(a) Simple curve
(b) Simple closed curve
(c) Polygon
(d) Convex polygon
(e) Concave polygon
Ans:
(a) Simple curve – 1, 2, 5, 6, 7
(b) Simple closed curve – 1, 2, 5, 6, 7
(c) Polygon – 1, 2
(d) Convex polygon – 2
(e) Concave polygon – 1
Q2. How many diagonals does each of the following have?
(a) A convex quadrilateral
Ans. Two
(b) A regular hexagon
Ans. 9
(c) A triangle
Ans. 0 (zero)
Q3. What is the sum of the measures of the angles of a convex quadrilateral? Why this property hold if the quadrilateral is not convex? (Make a non-convex quadrilateral and try!)
Ans. Angle sum of a convex quadrilateral = (4 – 2) × 180° = 2 × 180° = 360°
Since, quadrilateral, which is not convex, i.e. concave has same number of sides i.e. 4 as a convex quadrilateral have, thus, a quadrilateral which is not convex also hold this property. i.e. angle sum of a concave quadrilateral is also equal to 360°
Q4. Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.)
Ans. x, y and z will be complementary to 50°.
So, Required angle = 180° – 50° = 130°
Ans. z being opposite angle= 80°
x and y are complementary, x and y
= 180° – 80° = 100°
Ans. As angles on one side of a line are always complementary
So, x = 90°
So, y = 180° – (90° + 30°) = 60°
The top vertex angle of the above figure
= 60° × 2 = 120°
Hence,
bottom vertex Angle = 120° and z = 60°
Ans. y= 112°, as opposite angles are equal in a parallelogram
x= 180° – (112° – 40°) = 28°
As adjacent angles are complementary so angle of the bottom left vertex
=180° – 112° = 68°
So, z = 68° – 40° = 28°
Another way of solving this is as follows:
As angles x and z are alternate angles of a transversal so they are equal in measurement.
Q3. Can a quadrilateral ABCD be a parallelogram if
(i) ∠D = ∠B = 180°?
(ii) ∠AB = DC = 8 cm,
AD = 4cm and BC = 4.4cm?
(iii) ∠A = 70° and ∠C = 65°?
Ans. (i) It can be , but not always as you need to look for other criteria as well.
(ii) In a parallelogram opposite sides are always equal, here AD BC, so its not a parallelogram.
(iii) Here opposite angles are not equal, so it is not a parallelogram.
Q5. The measures of two adjacent angles of a parallelogram are in the ratio 3 : 2. Find the measure of each of the angles of the parallelogram.
Ans. Opposite angles of a parallelogram are always addupto 180°.
So, 180° = 3x + 2x
⇒ 5x = 180°
⇒ x = 36°
So angles are;
36° × 3 = 108° and 36° × 2 = 72°
Q6. Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram.
Ans. 90°, as they add up to 180°
Q7. The adjacent figure HOPE is a parallelogram. Find the angle measures x, y and z. State the properties you use to find them.
Ans. Angle opposite to y = 180° – 70° = 110°
Hence, y = 110°
x = 180° – (110° + 40°) = 30°,
(triangle’s angle sum)
z = 30° (Alternate angle of a transversal)
Q8. The following figures GUNS and RUNS are parallelograms. Find x and y. (Lengths are in cm)
Ans. As opposite sides are equal in a parallelogram
So, 3y – 1 = 26
⇒ 3y = 27
⇒ y = 9
Similarly, 3x = 18
⇒ x = 6
a quadrilateral
(b) Opposite sides are parallel so it is a parallelogram
(c) Diagonals bisect each other so it is a rhombus
(d) Opposite sides are equal and angles are right angles so it is a rectangle.
Q4. Name the quadrilaterals whose diagonals.
(a) bisect each other
(b) are perpendicular bisectors of each other
(c) are equal
Ans. Rhombus; because, in a square or rectangle diagonals don’t intersect at right angles.
Q5. Explain why a rectangle is a convex quadrilateral.
Ans. Both diagonals lie in its interior, so it is a convex quadrilateral.
Q6. ABC is a right-angled triangle and O is the mid point of the side opposite to the right angle. Explain why O is equidistant from A, B and C.
Ans. If we extend BO to D, we get a rectangle ABCD. Now AC and BD are diagonals of the rectangle.
In a rectangle diagonals are equal and bisect each other.
So, AC = BD
AO = OC
BO = OD
And AO = OC = BO = OD
So, it is clear that O is equidistant from A, B and C.
Answer:
8.6666
Step-by-step explanation:
2+3x+62 =90
64+3x =90
3x=90-64
3x =26
x=26/3
x=8.6666...