Question

date: 09-01-2025 per: 3
this is a 2-page document!

1. find the missing measure. diagram with x° and 65°
2. find the missing measure. diagram with 51° and x°
3. find the missing measures. diagram with 107°, x°, y°, z°
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 m∠1 = (5x + 9)° and m∠2 = (3x + 11)°, find the measure of each angle.
7. ∠1 and ∠2 are vertical angles. if m∠1 = (17x + 1)° and m∠2 = (20x − 14)°, find m∠2.
8. ∠k and ∠l are complementary angles. if m∠k = (3x + 3)° and m∠l = (10x − 4)°, find the measure of each angle.
9. if m∠p is three less than twice the measure of ∠q, and ∠p and ∠q are supplementary angles, find each angle measure.
10. if m∠b is two more than three times the measure of ∠c, and ∠b and ∠c are complementary angles, find each angle measure.

Explanation:

Problem 4:

Step1: Recall supplement definition

Supplementary angles sum to \(180^\circ\). Let the angle be \(A = 13^\circ\), its supplement \(S\) satisfies \(A + S = 180^\circ\).

Step2: Solve for supplement

\(S = 180^\circ - 13^\circ = 167^\circ\)

Step1: Recall complement definition

Complementary angles sum to \(90^\circ\). Let the angle be \(A = 38^\circ\), its complement \(C\) satisfies \(A + C = 90^\circ\).

Step2: Solve for complement

\(C = 90^\circ - 38^\circ = 52^\circ\)

Step1: Linear pair sum to \(180^\circ\)

\(m\angle1 + m\angle2 = 180^\circ\), so \((5x + 9) + (3x + 11) = 180\).

Step2: Simplify equation

\(8x + 20 = 180\), \(8x = 160\), \(x = 20\).

Step3: Find angle measures

\(m\angle1 = 5(20) + 9 = 109^\circ\), \(m\angle2 = 3(20) + 11 = 71^\circ\)

Answer:

\(167^\circ\)

Problem 5: