In a right triangle the measure of one acute angle is 4 times the difference of the measure of the other acute angle and 5. Find the measure of each acute angle

The sum of the acute angles in a right-angled triangle is 90.

The acute angles are 22 and 68 degrees

Let the acute angles be x and y, such that:

So, we have:

Substitute 4(x - 5) for y

Open brackets

Add x and 4x

Add 20 to both sides

Divide both sides by 5

Recall that:

So, we have:

Hence, the acute angles are 22 and 68 degrees

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The measures are 22 and 68 degrees

Step-by-step explanation:

for a right triangle, the total angle measure gives 90

Let one of the acute angle be x and the other be y

The measure of one of the acute angle is 4 times the the difference of the measure of the other angle and 5

x = 4(y-5)

Also x + y = 90

Put i into ii

4(y-5) + y = 90

4y-20 + y = 90

5y-20 = 90

5y = 90 + 20

5y = 110

y = 110/5

y = 22

But;

x = 4(y-5)

x = 4(22-5)

x = 4(17)

x = 68

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step-by-step explanation: