Question

I WILL MARK THE BRAINLIEST WHO ANSWERS MORE QUESTIONS.

Answer 1

Answer is 27 degree
(Option B)

Answer 2

For 1st pic attached;
Solution:
Let the unknown angle of 1st square be A & 3rd square be B.

Then according to the given conditions, we get
36 + A + x = 90
or A + x = 90 - 36
or A + x = 54 ........E1
similarly, B + x = 63 ........E2
& A + B + x = 90 ........E3

Therefore, A = 54-x ......(from E1)
& B = 63-x ........(from E2)
substituting A & B in E3, we get
(54-x) + (63-x) + x = 90
or 117 -x = 90
or x = 117-90
Therefore, x = 27°

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For 2nd pic attached;
Solution:
Let the side AB, BC & AC be c, a & b.

To find the angles, we will have to use the property of cosine, ie,
For angle A, cos A = (b^2 + c^2 - a^2)/2bc
cos A = (25^2 + 27^2 -24^2)/ 2×25×27
cos A = 778/1350 = 0.576
Therefore, angle A = cos-1 (0.576) = 54°49'

For angle B, cos B = (c^2 + a^2 - b^2)/2ca
cos B = (27^2 + 24^2 -25^2)/ 2×27×24
cos B = 680/1296 = 0.5247
Therefore, angle B = cos-1 (0.5247) = 58°21'

Now we know that the sum of the angles of a triangle is 180°
Therefore, angle C = 180° - 54°49' - 58°21'
= 66°50'

Therefore, angle A = 54°49' is the smallest angle of the given triangle.

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For 3rd pic attached;
Solution:
From fig.
In ∆TCE,
angle T = 180-35-31 = 114.

In ∆BPT,
angle T = 180-114 = 66.

Now, external angle at point T,
= 180-66 = 114

Therefore, angle x = 360-114-66-114 = 66°

Therefore, it is conclusive that angle x in ∆ATS = angle T in ∆BPT.

Similarly,
angle S in ∆ATS = angle S in ∆ERS .........1

In ∆SBD,
angle S = 180-30-36 = 114

Therefore, angle S in ∆ERS = 180-114 = 66 ........2

Therefore, angle S in ∆ATS = 66 ..........(from 1 &2)

Therefore, angle y = 180-66-66 = 48°

Hence, angle x = 66°
angle y = 48°.

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For 4th pic attached;
Solution:
From the given fig.

Total length of the path
= 60 + (80-4)
= 136 cm

Therefore, Area of path
= 4 × 136
= 544 cm^2.


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For 5th pic attached;
Solution:
Area of ∆AFG = (8×10)/2
= 40 cm^2

Area of Trapezium DEBC
= (14+20)/2 × (28-16)
= 17 × 12
= 204 cm^2

Hence, the Area of shaded region = 40+204
= 244 cm^2.