Question

clarifying big ideas: congruence and equality
type the correct answer in each box. use numerals instead of words.
$105^{circ}+x^{circ}+2x^{circ}=\square^{circ}$
$m\angle t = \square^{circ}$
$m\angle r=\square^{circ}$

Explanation:

Step1: Sum of angles in a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(105^{\circ}+x^{\circ}+2x^{\circ}=180^{\circ}\).

Step2: Solve for \(x\)

Combine like terms: \(105 + 3x=180\).
Subtract \(105\) from both sides: \(3x=180 - 105\), \(3x = 75\).
Divide both sides by \(3\): \(x=\frac{75}{3}=25\).

Step3: Find \(m\angle T\)

Since \(x = 25\), \(m\angle T=x^{\circ}=25^{\circ}\).

Step4: Find \(m\angle R\)

Since \(x = 25\), \(m\angle R=2x^{\circ}=2\times25 = 50^{\circ}\).

Answer:

\(180\), \(25\), \(50\)