Questions: 29. If BD bisects angle ABC, m angle DBC=68 degrees, and m angle ABC=(6x-8) degrees, find the value of x. x= 31. The measure of angle G is six more than three times the measure of angle H. If angle G and angle H are complementary angles, find m angle H. m angle H=

29. If BD bisects angle ABC, m angle DBC=68 degrees, and m angle ABC=(6x-8) degrees, find the value of x.
x=

31. The measure of angle G is six more than three times the measure of angle H. If angle G and angle H are complementary angles, find m angle H.
m angle H=

Transcript text: 29. If $\overline{B D}$ bisects $\angle A B C, m \angle D B C=68^{\circ}$, and $m \angle A B C=(6 x-8)^{\circ}$, find the value of $x$. \[ x= \] 31. The measure of $\angle G$ is six more than three times the measure of $\angle H$. If $\angle G$ and $\angle H$ are complementary angles, find $m \angle H$. \[ m \angle H= \]

Solution

Solution Steps

Step 1: Understand the problem

We need to find the value of $ x $ given that $ BD $ bisects $ \angle ABC $, $ m\angle DBC = 68^\circ $, and $ m\angle ABC = (6x - 8)^\circ $.

Step 2: Use the bisector property

Since $ BD $ bisects $ \angle ABC $, it means $ \angle ABD = \angle DBC $. Therefore, $ m\angle ABD = m\angle DBC = 68^\circ $.

Step 3: Set up the equation

Since $ \angle ABC $ is bisected into two equal parts, we have: \[ m\angle ABC = m\angle ABD + m\angle DBC \] \[ (6x - 8)^\circ = 68^\circ + 68^\circ \] \[ (6x - 8)^\circ = 136^\circ \]

Step 4: Solve for $ x $

\[ 6x - 8 = 136 \] \[ 6x = 136 + 8 \] \[ 6x = 144 \] \[ x = \frac{144}{6} \] \[ x = 24 \]