Question

please answer this question​

Answer 1

Answer:

1) 120°

2) 60°

3) 45°

4) 35°

5)40°

8) 25°

9)10

Answer 2

1.a

2.b

3.d

4.d

5.a

6.d

7.c

8.d

9.a

10.b

Solutions :-

1)

Given that

l || m

t is a transversal

We have ∠z and 60° are the interior angles on the same side to the transversal .

Therefore, ∠z and 60° are Supplementary angles.

=> ∠z+60° = 180°

=> ∠z = 180°-60°

=> ∠z = 120°

2)

Given that

l || m

t is a transversal

We have ∠x and 60° are the alternative interior angles.

Therefore, ∠x and 60° are equal.

=> ∠x = 60°

3)

Let the angle be X°

The complement of X° = 90°-X°

Given that

The angle = 4 times to its complement

=> X° = 4(90°-X°)

=> X° = 360°-4X°

=> X°+4X° = 360°

=> 5X° = 360°

=> X° = 360°/5

=> X° = 72°

The angle is 72°

4)

Given that

125° is the exterior angle of the triangle

x° and 90° are the opposite interior angles of 125°

=> x°+90° = 125°

=> x° = 125°-90°

=> x° = 35°

5)

Given that

In ∆XYZ, XY = YZ

=> ∠X = ∠Z

Since, The angles opposite to equal sides are equal.

Let ∠X = ∠Z = A°

Given that ∠Y = 100°

We know that

The sum of the three interior angles in a triangle is 180°

=> ∠X + ∠Y + ∠Z = 180°

=> A°+100°+A° = 180°

=> 2A° +100° = 180°

=> 2A° = 180°-100°

=> 2A° = 80°

=> A° = 80°/2

=> A° = 40°

Therefore, ∠X = ∠Z = 40°

∠Z = 40°

6)

Given that

In ∆ PQR, ∠P = 90° , ∠Q = 30° and ∠R = x°

We know that

The sum of the three interior angles in a triangle is 180°

=> ∠P + ∠Q + ∠R = 180°

=> 90°+30°+x° = 180°

=> 120°+x° = 180°

=> x° = 180°-120°

=> x° = 60°

7)

In ∆ ADC and ∆ ABC

∠CAD = ∠CAB

AC = AC

∠ACD = ∠ACB

By ASA Congruency rule ,∆ ACD and ∆ABC are Congruent triangles.

8)

Given that

Total number of children in a class = 40

Number of boys in the class = 10

The percentage of boys =

(No. of boys / Total no.of children)×100

= (10/40)×100

=> 100/4

= 25

The percentage of boys in the class = 25%

9)

Given that

Total number of children in a class = 40

Number of children like foot ball

= 25% of total number of children

= (25/100)×40

= (1/4)×40

= 40/4

= 10

No. of children who likes to play foot ball is 10

10)

Given that

The Cost Price of the coat = Rs. 7600

Sales tax on it = 4%

= 4% of 7600

= 4% × 7600

= (4/100)×7600

= 4×76

= Rs. 304

The sales tax is Rs. 304