Question

The measures of an angle and its supplement differ by 40°. What are the measures of the angles? Hint: an angle and its supplement have degree measures whose sum is 180°.

a. Y + (y − 40) = 180; 70°, 30°
b. 2y + (y + 40) = 180; 40°, 140°
c. Y + (y − 40) = 180; 70°, 110°
d. Y + (y − 40) = 180; 60°, 120

Answer 1

Assume y > x

Let the two angles be x and y

then, x + y = 180° ----------------- (i)

It is given the difference between angles is 40 °

So, y-x = 40

x= y-40

now equation (i) becomes

y-40+y = 180°

2y - 40 = 180°

2y = 220°

y = 110°

As x = y - 40

So x = 110-40

x = 70°

Hence the two angles are 110° and 70°

So the correct answer is option C