Question

PLEASE HELP WITH BOTH QUESTIONS ASAP AND EXPLAIN

Answer 1

a = 18

b = 56

Explanation:

Since we know that the sum of angles of a triangle is 180 degrees,

To find a, we look at the triangle at the left,

It must satisfy,

a + 63 + 99 = 180

a = 180 - 63 - 99

a = 18

For b,

we note that the angle supplementary to 99 is, (since adding them both gives a straight line i.e. adding them must equal 180),

i.e., lets call the angle x,

then,

99 + x = 180

x = 180 -99

x = 81

then for the triangle on the right, we have,

b + 43 + 81 = 180

b = 180 - 43 - 81

b = 56

We could have also found b by considering the entire (big) triangle that is cut into two,

in this case,

63 + b + (a + 43) = 180

63 + b + (18 + 43) = 180

b = 180 - 63 - 18 - 43

b = 56

Hence we get the same answer

Answer 2

b = 56 , a = 18

Explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

99° is an exterior angle to the triangle on the right of the diagram , then

43 + b = 99 ( subtract 43 from both sides )

b = 56

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the sum of the 3 angles in a triangle is 180°

sum the 3 angles and equate to 180

a + 99 + 63 = 180

a + 162 = 180 ( subtract 162 from both sides )

a = 18