Question

name: _
unit 1: geometry basics
date: _ per: _ homework 6: angle relationships
this is a 2 - page document!

1. find the missing measure.
2. find the missing measure.
3. find the missing measures.
4. if the measure of an angle is 13°, find the measure of its supplement.
5. if the measure of an angle is 38°, find the measure of its complement.
6. ∠1 and ∠2 form a linear pair. if ( mangle1=(5x + 9)^{circ} ) and ( mangle2=(3x + 11)^{circ} ), find the measure of each angle.
7. ∠1 and ∠2 are vertical angles. if ( mangle1=(17x + 1)^{circ} ) and ( mangle2=(20x - 14)^{circ} ), find ( mangle2 ).
8. ∠k and ∠l are complementary angles. if ( mangle k=(3x + 3)^{circ} ) and ( mangle l=(10x - 4)^{circ} ), find the measure of each angle.
9. if ( mangle p ) is three less than twice the measure of ( angle q ), and ( angle p ) and ( angle q ) are supplementary angles, find each angle measure.
10. if ( mangle b ) is two more than three times the measure of ( angle c ), and ( angle b ) and ( angle c ) are complementary angles, find each angle measure.

Explanation:

Step1: Use the property of linear pairs

Since \(∠1\) and \(∠2\) form a linear pair, \(m∠1 + m∠2=180^{\circ}\).
Given \(m∠1=(5x + 9)^{\circ}\) and \(m∠2=(3x + 11)^{\circ}\), we have the equation \((5x + 9)+(3x + 11)=180\).

Step2: Simplify the equation

Combine like - terms: \(5x+3x+9 + 11=180\), which simplifies to \(8x+20 = 180\).
Subtract 20 from both sides: \(8x=180 - 20=160\).
Divide both sides by 8: \(x=\frac{160}{8}=20\).

Step3: Find \(m∠1\) and \(m∠2\)

Substitute \(x = 20\) into \(m∠1=(5x + 9)^{\circ}\): \(m∠1=(5\times20+9)^{\circ}=(100 + 9)^{\circ}=109^{\circ}\).
Substitute \(x = 20\) into \(m∠2=(3x + 11)^{\circ}\): \(m∠2=(3\times20+11)^{\circ}=(60+11)^{\circ}=71^{\circ}\).

Answer:

\(m∠1 = 109^{\circ}\) and \(m∠2 = 71^{\circ}\)