two angles are complementary the larger angle is 3degree less than twice the measure of the smaller angle find the measure of each angle
Share
two angles are complementary the larger angle is 3degree less than twice the measure of the smaller angle find the measure of each angle
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Verified answer
Correct Question:
Two angles are complementary. The larger angle is 3 degrees less than twice the measure of the smaller angle. Find the measure of each angle.
Solution:
The basic concept to be kept in mind is that:
The sum of two complementary angles is 90°. Therefore the constituent complements will both have measures smaller than 90° and will also add upto 90°.
Statement: The larger angle is 3 degrees less than twice the measure of the smaller angle.
Let the smaller angle be x. This means that the larger angle is 3 degrees less than 2x.
Larger angle = 2x - 3
As said before, sum of two complementary angles is 90°.
Forming an equation:
Therefore,
The measure of the smaller angle = x = 31°
The measure of the larger angle = 2x - 3
= (2 x 31) - 3
= 62 - 3
= 59°
So, the complementary angles are 31° and 59°.
⇒ Verification:
LHS:
= 31 + 59
= 90
RHS:
= 90
LHS = RHS
Hence verified!
Knowledge Bytes:
⇒ Complementary angles:
Those angles that add upto 90° are known as complementary angles. These angles are complement to each other. Together, they form a right angle.
⇒ Supplementary angles:
Those angles that add upto 180° are known as supplementary angles. These angles are supplement to each other. Together, they form a straight angle.
Answer:
Two angles are complementary. The larger angle is 3 degrees less than twice the measure of the smaller angle. Find the measure of each angle.
The basic concept to be kept in mind is that:
The sum of two complementary angles is 90°. Therefore the constituent complements will both have measures smaller than 90° and will also add upto 90°.
Statement: The larger angle is 3 degrees less than twice the measure of the smaller angle.
Let the smaller angle be x. This means that the larger angle is 3 degrees less than 2x.
Larger angle = 2x - 3
As said before, sum of two complementary angles is 90°.
Forming an equation:
x+2x−3=90
3x−3=90
3x=90+3
3x=93
x= 93/3
x=31
Therefore,
The measure of the smaller angle = x = 31°
The measure of the larger angle = 2x - 3
= (2 x 31) - 3
= 62 - 3
= 59°
So, the complementary angles are 31° and 59°.
⇒ Verification:
LHS:
= 31 + 59
= 90
RHS:
= 90
LHS = RHS
Hence verified!
Knowledge Bytes:
⇒ Complementary angles:
Those angles that add upto 90° are known as complementary angles. These angles are complement to each other. Together, they form a right angle.
⇒ Supplementary angles:
Those angles that add upto 180° are known as supplementary angles. These angles are supplement to each other. Together, they form a straight angle.