Question

1. ∠1 and ∠2 form a linear pair. the measure of ∠2 is six more than twice the measure of ∠1. find m∠2.
2. ∠j and ∠k are complementary angles. the measure of ∠j is 18 less than the measure of ∠k. find the measures of both angles.
3. if (overrightarrow{uw}) bisects ∠tuv, (m∠tuw = 13x - 5) and (m∠wuv = 7x + 31), find the value of x.
4. if (overrightarrow{mo}) bisects ∠pmn, (m∠pmn = 74^{circ}) and (m∠omn = 2x + 7), find the value of x.
5. if (overrightarrow{ef}) bisects ∠ceb, (m∠cef = 7x + 21) and (m∠feb = 10x - 3), find the measure of ∠deb.

Explanation:

Step1: Use the angle - bisector property

Since \(\overrightarrow{UW}\) bisects \(\angle TUV\), then \(m\angle TUW=m\angle WUV\).
So, \(13x - 5=7x + 31\).

Step2: Solve the equation for \(x\)

Subtract \(7x\) from both sides: \(13x-7x - 5=7x-7x + 31\), which gives \(6x-5 = 31\).
Add \(5\) to both sides: \(6x-5 + 5=31 + 5\), so \(6x=36\).
Divide both sides by \(6\): \(x=\frac{36}{6}=6\).

Answer:

\(x = 6\)