Math, asked by vishnucars2014, 10 months ago

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

Answered by rudransh45
2

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.

Answered by sailasya001
2

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...

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