Question

this question has two parts. first, answer part a. then, answer part b.
part a
consider the triangle shown.
what is the value of ( x )?
( x = square )
part b
which of the following are angle measures of the triangle? select all that apply.
a) ( 13^circ )
b) ( 23^circ )
c) ( 33^circ )
d) ( 54^circ )
e) ( 113^circ )

Explanation:

Step1: Sum angles to 180°

The sum of interior angles in a triangle is $180^\circ$. So set up the equation:
$$(4x + 21) + (2x + 8) + (x - 10) = 180$$

Step2: Simplify left side

Combine like terms:
$$4x+2x+x + 21+8-10 = 180$$
$$7x + 19 = 180$$

Step3: Solve for x

Subtract 19 from both sides, then divide by 7:
$$7x = 180 - 19$$
$$7x = 161$$
$$x = \frac{161}{7} = 23$$

Step4: Calculate each angle

Substitute $x=23$ into each angle expression:

• $4x+21 = 4(23)+21 = 92+21 = 113^\circ$
• $2x+8 = 2(23)+8 = 46+8 = 54^\circ$
• $x-10 = 23-10 = 13^\circ$

Answer:

Part A: $x=23$
Part B: A) $13^\circ$, D) $54^\circ$, E) $113^\circ$