Question

what is deficit and budget?

ABCD is a parallelogram. Angle B = 5x + 25 degree and Angle D = 8x - 5 degree. Find x and angle C . ztypxeuoah ​

Answer 1

Answer:

Deficit means loss

budget means an estimate of income and expenditure for a set period of time.

Answer 2

Q. 1 Deficit and Budget :

Deficit : An amount by which an amount falls short of the required amount.

Budget : A budget is an estimate of revenue and expenditure over a specified future period.

A budget deficit is the amount by which an individual, business, or government's income fall short of the expectations set forth in its budget over a given time period.

Q. 2 ABCD is a parallelogram. Angle B = 5x + 25 degree and Angle D = 8x - 5 degree. Find x and angle C.

Solution : Here, a/c to question

• ∠ B = 5x + 25 ----{1}
• ∠ D = 8x - 5 ----{2}

Here we know that; the opposite angles of the parallelogram are congruent.

Hence, a/c to figure; ∠ A = ∠ C and ∠B = ∠ D ----{3}

➜ ∠ B = ∠ D

➜ 5x + 25 = 8x - 5

➜ 5x - 8x = - 5 - 25

➜ - 3x = - 30

➜ 3x = 30

➜ x = 30/3

➜ x = 10

Now, put value of x in eq. {1} and eq. {2}

➜ ∠ B = 5x + 25

➜ ∠ B = 5 * 10 + 25

➜ ∠ B = 50 + 25

➜ ∠ B = 75⁰

and

➜ ∠ D = 8x - 5

➜ ∠ D = 8 * 10 - 5

➜ ∠ D = 80 - 5

➜ ∠ D = 75⁰

Parallelograms have angles totalling 360⁰.

Hence,

➜ ∠ A + ∠ B + ∠ C + ∠ D = 360⁰

from {3}

➜ ∠ A + ∠ A + 75⁰ + 75⁰ = 360⁰

➜ 2 * ∠ A + 150⁰ = 360⁰

➜ 2 * ∠ A = 360⁰ - 150⁰

➜ 2 * ∠ A = 210

➜ ∠ A = 210/2

➜ ∠ A = 105⁰

∴ ∠ A = ∠ C = 105⁰

Answer : Hence, the of of x is 10 and the angle C is 105⁰.

{More info : Properties of the parallelogram

• The opposite sides are parallel and congruent
• The opposite angles are congruent
• The consecutive angles are supplementary
• If any one of the angles is a right angle, then all the other angles will be at right angle
• The two diagonals bisect each other
• Each diagonal bisects the parallelogram into two congruent triangles
• The Sum of square of all the sides of parallelogram is equal to the sum of square of its diagonals }