Question

Angle A is complement of Angle B. M Angle A = (2x-3) and M Angle B = (3x-2). Find M Angle A.

Answer 1

Answer: m∠A = 35°

Explanation:

In order to find the measure of ∠A, we'll set up an equation.

Since the angles are complementary, their sum is 90°. Therefore,

`m\angle A+ m\angle B=90`

`2x-3+3x-2=90`

Solve for x.

`2x+3x-3-2=90`

`5x-5=90`

`5x=95`

`x=19`

Next, plug x = 19 into the measure of angle a, which is 2x -3:

`2(19)-3`

`38-3`

`35`

Therefore, m∠A = 35°.

Answer 2

They are complementary angles which means their sum is 90°

`: \implies\tt A+B=90`

We have,

• A = (2x-3)
• B = (3x-2)

Put the values;

`\longmapsto \sf \: (2x - 3) + (3x - 2) = 90`

`\longmapsto \sf \: 2x - 3+ 3x - 2 = 90`

`\longmapsto \sf \: 5x - 3 - 2 = 90`

`\longmapsto \sf \: 5x -5 = 90`

`\longmapsto \sf \: 5x = 95`

`\longmapsto \sf \: x = 19`

We know that,

`\red{ \tt \: A = 2x - 3}`

`\red{ \tt \: A = 2 * 19 - 3}`

`\boxed{ \underline{ \underline{ \red{ \tt \: A = 35°}}}}`