It is given that [tex]$\angle ABE$[/tex] and [tex]$\angle DBC$[/tex] are vertical angles. By the Vertical Angles Theorem, [tex]$\angle ABE$[/tex] is congruent to [tex]$\angle DBC$[/tex]. By the definition of congruence, the measure of [tex]$\angle ABE$[/tex] must equal the measure of [tex]$\angle DBC$[/tex]. Then, by the substitution property of equality, [tex]$2x + 6 = x + 10$[/tex]. Applying the subtraction property of equality gives [tex]$x = 4$[/tex].

Question

valeriavaldez2007 valeriavaldez2007

23-07-2024
Mathematics

Answered

It is given that [tex]$\angle ABE$[/tex] and [tex]$\angle DBC$[/tex] are vertical angles. By the Vertical Angles Theorem, [tex]$\angle ABE$[/tex] is congruent to [tex]$\angle DBC$[/tex]. By the definition of congruence, the measure of [tex]$\angle ABE$[/tex] must equal the measure of [tex]$\angle DBC$[/tex]. Then, by the substitution property of equality, [tex]$2x + 6 = x + 10$[/tex]. Applying the subtraction property of equality gives [tex]$x = 4$[/tex].

Answer :

Other Questions

Round or oval candies filled with fruit preserves or cream and covered with chocolate are called?

Three fifths Of a number plus One fourth Of a number Is 34. Find The number.

Maggie bought 2 boxes of cupcakes for her daughters. She ate one cupcake herself and told her 3 daughters to share the remaining cupcakes equally. If there were

Bella serves pizza at her party. each pizza is cut into 6 equal slices. there are 13/6 pizzas left after three party is over. the slices are in 3 different pizz

Horace Bushnell is associated with which idea? a.religious liberalism b.religious fundamentalism c.religious intolerance d.religious liberty

Special, temporary committees of Congress for specific purposes are called a: select committees b: joint committees c: standing committees d: conference committ

Why did White Settlers believe they could buy land from American Indians?

A scientist is studying the population decline of cheetahs in Africa and the Middle East over the past several decades. Which best describes this situation? a c

12. Which was a part of the Roman Republic's representative government? citizen assemblies fasces permanent dictators Roman legions

What event led to Theodore Roosevelt becoming President? A. Elections were rigged in several states. B. The election was tied and a re-vote resulted in Roosevel

GinnyAnswer GinnyAnswer · Answer 1 · 2024-07-23T22:42:39-04:00

It is given that [tex]$\angle ABE$[/tex] and [tex]$\angle DBC$[/tex] are vertical angles. By the vertical angles theorem, [tex]$\angle ABE$[/tex] is congruent to [tex]$\angle DBC$[/tex]. By the definition of congruence, the measure of [tex]$\angle ABE$[/tex] must equal the measure of [tex]$\angle DBC$[/tex]. Then, by the substitution property of equality, we can set up the equation [tex]$2x + 6 = x + 10$[/tex]. Applying the subtraction property of equality gives [tex]$x = 4$[/tex]. Hence, we have proven that [tex]$x = 4$[/tex].