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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=

Verified Answer :

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=\(66\°\) ----> 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 \(180\°\)

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 \(60\°\)

so

∠CBD=\(60\°\)

Step 3

Find the measure of the angle ∠ABC

∠ABC=∠ABD+∠DBC

substitute the values

∠ABC=\(48\°+66\°=114\°\)

therefore

the answer is

the measure of the angle ∠ABC is \(114\°\)


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°

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