Answer:
m∠ABD = 96
Step-by-step explanation:
Given
m∠ABC = 5/2x + 18
m∠CBD = 4x
Required
Determine m∠ABD
From the given parameters, we understand that:
∠ABC ≅ ∠CBD
This implies that:
[tex]\frac{5}{2}x + 18 = 4x[/tex]
Collect Like Terms
[tex]\frac{5}{2}x - 4x =- 18[/tex]
Take LCM
[tex]\frac{5x - 8x}{2} = -18[/tex]
[tex]\frac{-3x}{2} = -18[/tex]
Cross Multiply
[tex]-3x = -18 * 2[/tex]
[tex]-3x = -36[/tex]
Divide through by -3
[tex]x = 12[/tex]
m∠ABD can be calculated using:
m∠ABD = m∠ABC + m∠CBD
[tex]ABD = \frac{5}{2}x + 18 + 4x[/tex]
Substitute 12 for x
[tex]ABD = \frac{5}{2} * 12 + 18 + 4 * 12[/tex]
[tex]ABD = 30 + 18 + 48[/tex]
[tex]ABD = 96[/tex]
Hence;
m∠ABD = 96
