Question

Two angles are adjacent and form an angle of $ {100^ \circ } $ . The larger is $ {20^ \circ } $ less than five times the smaller. The larger angle is
A. $ {90^ \circ } $
B. $ {70^ \circ } $
C. $ {80^ \circ } $
D. $ {75^ \circ } $

Answer 1

Hint: Let the smaller of the two adjacent angles be x and the larger of the two adjacent angles be y. Five times of the smaller angle can be written as 5x and the larger angle is $ {20^ \circ } $ less than five times the smaller this means y is equal to $ 5x - {20^ \circ } $ . Add x and y and equate this sum to $ {100^ \circ } $ , to find the value of the larger angle and the smaller angle.

Complete step-by-step answer:
We are given that two angles are adjacent and form an angle of $ {100^ \circ } $ and the larger is $ {20^ \circ } $ less than five times the smaller.
We have to find the measure of the larger angle.
We are given that the sum of larger and smaller angles is $ {100^ \circ } $ .
Let the smaller angle be x and the larger angle be y.
Larger angle is $ {20^ \circ } $ less than five times the smaller, this means y is equal to $ 5x - {20^ \circ } $
And as given $ x + y = {100^ \circ } $
On substituting the value of y in terms of x, we get $ x + 5x - {20^ \circ } = {100^ \circ } $
 $ \Rightarrow 6x - {20^ \circ } = {100^ \circ } $
 $ \Rightarrow 6x = {100^ \circ } + {20^ \circ } = {120^ \circ } $
 $ \therefore x = \dfrac{{{{120}^ \circ }}}{6} = {20^ \circ } $
The value of x, the smaller angle, is $ {20^ \circ } $
The larger angle y is $ 5x - {20^ \circ } = 5\left( {{{20}^ \circ }} \right) - {20^ \circ } = {100^ \circ } - {20^ \circ } = {80^ \circ } $
So, the correct answer is “Option C”.

Note: In this type of questions, we can consider the angles as any variables not only x and y. To verify whether the obtained result is correct or not, just add the smaller angle to the larger angle and the sum must equal $ {100^ \circ } $ . Any of the two angles must not exceed $ {100^ \circ } $ . If exceeded, then the answer we got is wrong. Make sure that the sign of the angles is positive as the measure of angles cannot be negative.