Question

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

Answer 1

Answer:

x = 65

y = 25

Step-by-step explanation:

x - y = 40

x + y = 90

x = 90 - y

90 - y - y = 40

-2y = 40 - 90

-2y = -50

y = -50/-2

y = 25

x - y = 40

x = 40 + y

x = 40 + 25

x = 65

Answer 2

Let the measure of the greater angle be x°.

The difference between the measures of the complementary pair is 40°.

$\therefore$ the measures of smaller angle is (x - 40)°

We know, the sun of the measures of complementary angles is 90°.

$\therefore \sf{x + (x - 40) = 90 \degree} \\ \\ : \implies\sf{ \frac{x + x - 40}{2x} } \\ \\ \sf{: \implies 90 + 40} \\ \sf{: \implies 2x = 130} \\ \\ \sf{: \implies x = { \cancel\frac{130}{2} }} \\ \sf{: \implies 65} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \mathfrak{ \underline{ \red{x = 65}}}}$

$\therefore$ measure of greater angle is 65° and the ꜱᴍᴀʟʟᴇʀ

angle = x - 40

⠀⠀⠀⠀= 65 - 40

⠀⠀⠀⠀= 25°

→ The measures of the two complementary angles are 65° & 25°.