dance76326
contestada

An equilateral triangle and an isosceles triangle share a common side. What is the measure of angle ABC? I need help with question 13 please asap!

An equilateral triangle and an isosceles triangle share a common side What is the measure of angle ABC I need help with question 13 please asap class=

Respuesta :

calculista

Step 1

Find the measure of the vertex angle ∠ABD of an isosceles triangle

we know that

An isosceles triangle has two equal sides and two equal angles

In this problem

∠ABD=∠BAD=[tex]66\°[/tex] ----> the angles of the base are equals

Find the measure of the vertex angle

∠ABD=[tex]180\°-2*66\°=48\°[/tex] ------> the sum of the internal angles of a triangle is equal to [tex]180\°[/tex]

Step 2

Find the measure of the angle  ∠CBD in the equilateral triangle

we know that

A equilateral triangle has three  equal sides and three equal angles

The measure of the internal angle in a equilateral triangle is [tex]60\°[/tex]

so

∠CBD=[tex]60\°[/tex]

Step 3

Find the measure of the angle ∠ABC

∠ABC=∠ABD+∠DBC

substitute the values

∠ABC=[tex]48\°+66\°=114\°[/tex]

therefore

the answer is

the measure of the angle ∠ABC is [tex]114\°[/tex]


aksnkj

Answer:

The measure of the angle ∠ABC is 108°

Step-by-step explanation:

Find the measure of the vertex angle ∠ABD of an isosceles triangle

we know that

An isosceles triangle has two equal sides and two equal angles

In this problem

∠BDA=∠BAD= 66° ----> the angles of the base are equals

Find the measure of the vertex angle

∠ABD = 180° - 2×66° = 48° (the sum of the internal angles of a triangle is  

                                             equal to 180°)

then,

Find the measure of the angle  ∠CBD in the equilateral triangle

we know that

A equilateral triangle has three  equal sides and three equal angles

The measure of the internal angle in a equilateral triangle is 60°

so

∠CBD= 60°

Find the measure of the angle ∠ABC

∠ABC=∠ABD+∠DBC

substitute the values

∠ABC= 48°+60° = 108°

Therefore

The answer is 108°

The measure of the angle ∠ABC is 108°

For more information:

https://brainly.com/question/17520847?referrer=searchResults

Otras preguntas