Question

The difference between the measures of the two angles of a complementary pair is 40 degrees. Find the measure of these two angles.

Answer 1

Answer:

Answer is in the picture.

Answer 2

★ Question:

The difference between the measures of the two angles of a complementary pair is 40°. Find the measure of these two angles.

★ Given Information:

$\implies$ The difference between the measures of the two angles of a complementary pair is 40 degrees.

★ To Find:

The measure of these two remaining angles.

★ Solution:

Let the measure of the greater angle be x°

The difference between the measures of the two angles of a complementary pair is 40°

∴ the measure of the smaller angle is (x - 40)°

We know that,

The sum of the measures of a complementary angle is 90°

$\implies \sf{x + (x - 40) = 90^\circ}$

$\implies \sf{x + x - 40 = 90^\circ}$

$\implies \sf{2x = 90 + 40}$

$\implies \sf{2x = 130}$

$\implies \sf{x = \dfrac{\cancel{130}}{\cancel{2}} }$

$\implies \underline{\boxed{\sf{\orange{ x = 65 }}}}$

     

The measure of the greater angle is 65° and the smaller angle,

$\implies \sf{x - 40}$

$\implies \sf{65 - 40}$

$\implies \underline{\boxed{\sf{\orange{ 25 }}}}$

   

$\underline{\sf{\therefore \; the \; measures \; of \; the \; two \; complementary \; angle \; are \; 65^\circ \; \& \; 25^\circ}}$