Question

If angle 1 and angle 2 are complementary angles and if the measures of angle 1 is 8 more than the measure of angle 2 determine the measures of angle 1 and 2

Answer 1

Answer:

41° and 49°

Step-by-step explanation:

Given:

Angle 1 and angle 2 are complementary angles.

The measures of angle 1 is 8 more than the measure of angle 2.

Question asked:

Determine the measures of angle 1 and 2.

Solution:

Let ∠1 = $x$

Then ∠2 = $x+8$   (given)

As we know that sum of complementary angles are 90° and here given that angle 1 and angle 2 are complementary angles which means,

∠1 + ∠2 = 90°

$x+x+8=90$°

$2x +8=90$°

Subtracting both sides by 8,

$2x=90$°$-8$

$2x = 82$°

Dividing both sides by 2,

$x=41$°

∠1 = $x=41$°

∠2 = $x+8$

∠2 = $41+8$ = 49°

Therefore, the measures of angle 1 and 2 are 41° and 49°