Question

1. in the figure, m∠abd = 100°. find m∠cbd and m∠abc.

a
c
(4x + 2)°
(3x - 7)°
b
d

Explanation:

Step1: Set up an equation based on angle - sum

Since $\angle ABD=\angle ABC+\angle CBD$, we have $(4x + 2)+(3x-7)=100$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $4x+3x+2 - 7=100$, which simplifies to $7x-5 = 100$.

Step3: Solve for $x$

Add 5 to both sides of the equation: $7x=100 + 5=105$. Then divide both sides by 7: $x=\frac{105}{7}=15$.

Step4: Find $\angle CBD$

Substitute $x = 15$ into the expression for $\angle CBD$: $\angle CBD=(3x-7)^{\circ}=(3\times15 - 7)^{\circ}=(45-7)^{\circ}=38^{\circ}$.

Step5: Find $\angle ABC$

Substitute $x = 15$ into the expression for $\angle ABC$: $\angle ABC=(4x + 2)^{\circ}=(4\times15+2)^{\circ}=(60 + 2)^{\circ}=62^{\circ}$.

Answer:

$m\angle CBD = 38^{\circ}$, $m\angle ABC=62^{\circ}$