Answer all the questions!!
Answers
These Are your Answers :
1] Given, Angle QPS = 43°
As we know, Alternate angles are equal (when lines are parallel).
So, Angle PSR = Angle QPS = 43°
As we know, The sum of all three angles of a triangle is 180° , then :
Angle(R+S+m) = 180°
or, 27°+43°+m = 180°
or, 70°+m = 180°
or, m = 180°-70°
or, m = 110°
Hence, value of m = 110°
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2] As Given,
Ratio of a:b = 2:3,
Let, a = 2x and b = 3x
We know that, if two angles are formed on a same line, with one of their arms common, then they are called linear pair.
So, a+b = 180°
or, 2x+3x=180°
or, 5x = 180°
or, x = 36°
Hence, b = 108°
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3] Always Remember : The exterior Angle of a triangle is always equal to sum of its opposite interior angles.
So, if opposite interior Angles are 43° and 27°,
Hence, exterior angle = 43°+27°
or, exterior Angle = 70°
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4] as we can clearly see, x is exterior angle of the triangle AOC, and
it's opposite angle are :ACO and AOC.
So, x = ACO +AOC
or, x = 80°+40°
or, x = 120°
As we can see, y is the exterior angle if the triangle DOB,
it's opposite angle are : ODB, BOD.
BOD is vertically opposite to AOC
or, BOD = AOC = 40°
So, y = BOD+OBD
or, y = 40°+70°
or, y = 110°
Hence, x+y = 110°+120°
or, x+y = 230°
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4) Let the angles be :
- x
- x+14°
So, x+(x+14°) = 90°
or, 2x+14°=90°
or, 2x = 76°
or, x = 38°
So, the angles are
- x = 38°
- x+14 = 52° .
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5] As we can see,
in triangle ABC, angle ACB = 90°
and, angle BAC = 40°
so,
ABC+BAC+ACB = 180°
or, ABC + 40°+90° = 180°
or, ABC + 130° = 180°
or, ABC = 50°
Now, in triangle BDE,
Angle EBD = 50°
Angle BED = 100°
So,
BED+EBD+BDE = 180°
or, 50°+100°+x = 180°
or, 150°+x =180°
or, x = 30° .
So, x = 30°