Question

Help is needed for both of these. Please and thank u!

Answer 1

Answer:

1. x = 15° | y = 120°

2. x = 4.5 | y = 60°

Step-by-step explanation:

1. 4x° + 4x° + 4x° = 180° ( The sum of all interior angles of any triangle is equal to 180° )

$4x + 4x + 4x = 180 \\ 12x = 180 \\ x = \frac{180}{12} \\ x = {15}^{o}$

4x° + 4x° = y° ( An exterior angle of a triangle is equal to the sum of its two interior opposite angles. )

$4x + 4x = y \\ 4(15) + 4(15) = y \\ 60 + 60 = y \\ {120}^{o} = y$

2. y° + 60° + 60° = 180° ( The sum of all interior angles of any triangle is equal to 180° )

$y + 60 + 60 = 180 \\ y + 120 = 180 \\ y = 180 - 120 \\ y = {60}^{o}$

All three internal angles are also congruent to each other and are each 60°. Therefore this is a equilateral triangle.

Perimeter = 4x + 4x + 4x ( An equilateral triangle is a triangle with all three sides of equal length. )

$54 = 4x + 4x + 4x \\ 54 = 12x \\ \frac{54}{12} = x \\ x = 4.5$