Complementary angles definition geometry
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Answer:
The measure of middles angle is 113.5° .
Step-by-step explanation:
Given as :
The measure of the largest angle is 10 less than 5 time the smallest angle.
The measure of the middle angle is 6 more than twice the measure of the largest angle
Let The largest angle = L
Let The middle angle = M
Let The smallest angle = S
As per statement
Largest angle = 5 times smallest angle - 10
i.e L = 5 × S - 10 .....1
Again
Middle angle = twice largest angle + 6
i.e M = 2 × L + 6 ......2
Since for any Triangle sum of three angles = 180°
i.e ∠L + ∠M + ∠S = 180°
Or, ( 5 × S - 10 ) + ( 2 × L + 6 ) + S = 180°
Or, ( 5 × S - 10 ) + [ 2 × (5 × S - 10 ) + 6 ] + S = 180°
Or, 5 S - 10 + (10 S - 20 + 6) + S = 180°
Or, 5 S - 10 + 10 S - 20 + 6 + S = 180°
Or, (5 + 10 + 1) S - 24 = 180°
Or, 16 S = 180° + 24
Or, 16 S = 204
∴ S =
i.e S = 12.75
So, The measure of smallest angle = S = 12.75°
And
L = 5 × 12.75 - 10
i.e L = 53.75
So, The measure of Largest angle = L = 53.75°
And
M = 2 × L + 6
Or, M = 2 × 53.75 + 6
i.e M = 107.5 + 6 = 113.5
So, The measure of middles angle = M = 113.5°
Hence, The measure of middles angle is 113.5° . Answer