Question

. ∠ABC is adjacent to ∠CBD. If the m∠ABC=4x+23, m∠CBD=6x+7, and m∠ABD=130°, what is the measure of angle ABC?

Answer 1

Answer:

The measure of angle ABC is

$63 \degree$

Step-by-step explanation:

As illustrated in the diagram,we can conclude that m<ABC+m<CBD=m<ABD

This implies that

$4x + 23 + 6x + 7 = 130 \degree$

$4x+6x+23+7 =130 \degree$

$10x + 30=130 \degree$

$10x=130 \degree - 30 \degree$

$10x=100 \degree$

Dividing through by 10, we obtain

$x=10 \degree$

This implies

m<ABC=4x+27

$= 4(10)+23$

$=40+23$

$=63 \degree$

Therefore the measure of angle ABC is

$63 \degree$