Question

determine the following. 10 points two congruent angles isosceles trapezoid kmrc have measures (3x + 10)° and (5x − 10)°. what is the value of x? 2 4 6 8 10 12 20 25 30 what is the measure of angle m? 2 4 6 8 10 12 20 25 30 what is the measure of angle c? 2 4 6 8 10 12 20 25 30

Explanation:

Step1: Set angles equal (congruent)

$3x + 10 = 5x - 10$

Step2: Solve for x

$10 + 10 = 5x - 3x$
$20 = 2x$
$x = \frac{20}{2} = 10$

Step3: Calculate angle M

Substitute $x=10$ into $3x+10$:
$3(10) + 10 = 30 + 10 = 40^\circ$

Step4: Calculate angle C

In isosceles trapezoid, consecutive angles between bases are supplementary:
$180^\circ - 40^\circ = 140^\circ$

Answer:

1. The value of x: 10
2. The measure of angle M: $40^\circ$
3. The measure of angle C: $140^\circ$