josalineshepardson
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BRAINLIEST IF RIGHT AND ANSWER QUICK BTW 100 points!!!
1. In the isosceles trapezoid, what is the measure of ∠1?
50°
130°
25°
260°

2. What is the measure of ∠1?
87°
164°
97°
74°
Question 1 goes with the purple shape and question 2 goes with the green shape!

BRAINLIEST IF RIGHT AND ANSWER QUICK BTW 100 points 1 In the isosceles trapezoid what is the measure of 1 50 130 25 260 2 What is the measure of 1 87 164 97 74 class=
BRAINLIEST IF RIGHT AND ANSWER QUICK BTW 100 points 1 In the isosceles trapezoid what is the measure of 1 50 130 25 260 2 What is the measure of 1 87 164 97 74 class=

Respuesta :

[tex]\\ \rm\Rrightarrow <1+130=180[/tex]

[tex]\\ \rm\Rrightarrow <1=180-130=50°[/tex]

#2

[tex]\\ \rm\Rrightarrow <1+87+109+90=360[/tex]

[tex]\\ \rm\Rrightarrow <1+286=360[/tex]

[tex]\\ \rm\Rrightarrow <1=360-286[/tex]

[tex]\\ \rm\Rrightarrow <1=74°[/tex]

Solution (1):

We know that:

  • Sum of the angles in a quadrilateral = 360°
  • Base angles of a trapezoid are equal
  • Top angles of a trapezoid are equal

This means that:

  • [tex]130 + 130 + \angle1 + \angle1 = 360[/tex]

Let's simplify the equation to find ∠1.

Step-by step calculations:

Add the constants:

  • [tex]260 + \angle1 + \angle1 = 360[/tex]

Add the angles:

  • [tex]260 + 2\angle1 = 360[/tex]

Subtract 260 both sides:

  • [tex]260 - 260 + 2\angle1 = 360 - 260[/tex]
  • => [tex]2\angle1 = 100[/tex]

Divide 2 both sides:

  • => [tex]\frac{2\angle1}{2} = \frac{100}{2}[/tex]
  • => [tex]\bold{\angle1 = 50\°}[/tex]

Solution (2):

We know that:

  • Sum of the angles in a quadrilateral = 360°

This means that:

  • [tex]109 + 87 + 90 + \angle1 = 360\°[/tex]

Let's simplify the equation to find ∠1.

Step-by step calculations:

Simplify the LHS:

  • [tex]109 + 87 + 90 + \angle1 = 360\°[/tex]
  • => [tex]286 + \angle1 = 360\°[/tex]

Subtract 286 both sides:

  • => [tex]286 - 286 + \angle1 = 360 - 286[/tex]
  • => [tex]\angle1 = 360 - 286[/tex]

Simplify the RHS:

  • => [tex]\bold{\angle1 = 74\°}[/tex]

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