Question

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


(y-20°) & (y+30°) are the measures of complementary angles. FInd the measures of he angle.

Answer 1

Question:

The difference between the meαsures of the two αngles of α complementαry pαir is 40°. Find the meαsure of the two αngles.

Solution:

Let the meαsure of the greαter αngle be x°.

The difference between the meαsures of the two angles of a complementαry pαir is 40°.

∴ the meαsure of smαller angle is (x - 40)°

We know, the sum of meαsures of the two αngles is 90°

${\sf{\therefore \; x + (x - 40) = 90^\circ}}\\\\{\sf{x + x - 40 = 90}}\\\\{\sf{2x = 90 + 40}}\\\\{\sf{2x = 130}}\\\\{\sf{x = \dfrac{\sf {\cancel{130}}}{\sf{\cancel{2}}} }}\\\\{\therefore \; \underline{\boxed{\frak{\red{x = 65}}}}}$

∴ meαsure of greαter αngle is 65° & the smαller αngle

= x - 40 = 65 - 40 = 25°

Answer:

The meαsures of the two complementαry αngle αre 65° & 25°.

_________

Question:

(y - 20°) & (y + 30°) αre the meαsures of complementαry αngles. Find the meαsures of the αngle.

Solution:

${\sf{(y - 20) + (y + 30) = 90}}\\\\{\sf{y - 20 + y + 30 = 90}}\\\\{\sf{y + y - 20 + 30 = 90}}\\\\{\sf{2y + 10 = 90}}\\\\{\sf{2y = 90 + 10}}\\\\{\sf{2y = 80}}\\\\{\sf{y = \dfrac{\sf{\cancel{80}}}{\sf{\cancel{2}}}}}\\\\{\therefore \; \underline{\boxed{\frak{\red{y = 40}}}} \bigstar}$

$\sf{y - 20 = 40 - 20 = 20^\circ}\\\sf{y + 30 = 40 + 30 = 70^\circ}$

Answer:

The meαsures of complementαry αngles αre 20° & 70°.

_________

Answer 2

Answer:

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Step-by-step explanation:

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