In a right triangle, the measure of one acute angle is 2 times the sum of the measure of the other acute angle and 6. find the measure of each acute angle.

Let one acute angle be x

The other acute angle = 2(x + 6)

The sum of all the 3 angles in a triangle add up to 180

x + 2(x+ 6) + 90 = 180

x + 2x + 12 + 90 = 180

3x + 102 = 180

3x = 78

x = 26

one acute angle = x = 26

the other acute angle = 2(x + 6) = 2(26 + 6) = 64

The two acute angles are 26° and 64°

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.

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