Question

1. given: ∠abc is a right angle.

prove: x = 8
11x = 88
(6x + 5)° + (5x - 3)° = 90
∠abc = 90°
∠abc is a right angle
11x + 2 = 90
x = 8
∠abd + ∠cbd = ∠abc

Explanation:

Step1: Given

$\angle ABC$ is a right angle.

Step2: Definition of right angle

$\angle ABC = 90^{\circ}$

Step3: Angle Addition Postulate

$\angle ABD+\angle CBD=\angle ABC$

Step4: Substitution Property of Equality

$(6x + 5)^{\circ}+(5x - 3)^{\circ}=90^{\circ}$

Step5: Simplify

$6x+5 + 5x-3=90$
$11x+2 = 90$

Step6: Subtraction Property of Equality

$11x+2-2=90 - 2$
$11x=88$

Step7: Division Property of Equality

$\frac{11x}{11}=\frac{88}{11}$
$x = 8$

Answer:

$x = 8$