Question

in exercises, 5 – 8, find the angle measure. see 5. $angle 1$ is a complement of $angle 2$, and $mangle 1 = 23^circ$. find $mangle 2$. 6. $angle 3$ is a complement of $angle 4$, and $mangle 3 = 46^circ$. find $mangle 4$. 7. $angle 5$ is a supplement of $angle 6$, and $mangle 5 = 78^circ$. find $mangle 6$. 8. $angle 7$ is a supplement of $angle 8$, and $mangle 7 = 109^circ$. find $mangle 8$. find the measure of each angle. see example 4 & 5 9. diagram with angles $(3x + 5)^circ$ and $(10x - 7)^circ$ 10. diagram with right angle, angles $(15x - 2)^circ$ and $(7x + 4)^circ$

Explanation:

Problem 5:

Step1: Recall complementary angles

Complementary angles sum to \(90^\circ\), so \(m\angle1 + m\angle2 = 90^\circ\).

Step2: Substitute \(m\angle1 = 23^\circ\)

\(23^\circ + m\angle2 = 90^\circ\), then \(m\angle2 = 90^\circ - 23^\circ = 67^\circ\).

Step1: Recall complementary angles

Complementary angles sum to \(90^\circ\), so \(m\angle3 + m\angle4 = 90^\circ\).

Step2: Substitute \(m\angle3 = 46^\circ\)

\(46^\circ + m\angle4 = 90^\circ\), then \(m\angle4 = 90^\circ - 46^\circ = 44^\circ\).

Step1: Recall supplementary angles

Supplementary angles sum to \(180^\circ\), so \(m\angle5 + m\angle6 = 180^\circ\).

Step2: Substitute \(m\angle5 = 78^\circ\)

\(78^\circ + m\angle6 = 180^\circ\), then \(m\angle6 = 180^\circ - 78^\circ = 102^\circ\).

Answer:

\(67^\circ\)

Problem 6: