Question

what is the measure of angle trv? 20° 50° 60° 130°

Explanation:

Step1: Identify supplementary angles

Angles \( (2x + 10)^\circ \) and \( (x - 10)^\circ \) are supplementary (they form a linear pair), so their sum is \( 180^\circ \).

$$ (2x + 10) + (x - 10) = 180 $$

Step2: Solve for \( x \)

Simplify the left - hand side of the equation:

$$ 2x+10 + x-10=180 $$

$$ 3x=180 $$

Divide both sides by 3:

$$ x = \frac{180}{3}=60 $$

Step3: Find angle \( TRV \)

Angle \( TRV \) is \( (2x + 10)^\circ \). Substitute \( x = 60 \) into the expression:

$$ 2(60)+10=120 + 10=130^\circ $$

Wait, no, wait. Wait, actually, the two angles \( (2x + 10)^\circ \) and \( (x - 10)^\circ \) are adjacent and form a linear pair? Wait, no, looking at the diagram, maybe I made a mistake. Wait, actually, the angle \( TRV \) and the angle \( (x - 10)^\circ \): Wait, no, let's re - examine. Wait, the two angles \( (2x + 10)^\circ \) and \( (x - 10)^\circ \) are supplementary? Wait, no, maybe the angle \( TRV \) is \( (2x + 10)^\circ \) and the other angle is \( (x - 10)^\circ \), but actually, when we solve \( (2x + 10)+(x - 10)=180 \), we get \( x = 60 \). Then angle \( TRV \) is \( 2x + 10=2\times60 + 10 = 130 \)? But that's one of the options. Wait, but maybe I mixed up the angles. Wait, no, let's check again.

Wait, another approach: The two angles \( (2x + 10)^\circ \) and \( (x - 10)^\circ \) are supplementary. So \( (2x + 10)+(x - 10)=180\), \( 3x=180\), \( x = 60 \). Then angle \( TRV \): Wait, maybe I had the angle wrong. Wait, the angle \( TRV \) is \( (2x + 10)^\circ \), and when \( x = 60 \), \( 2\times60+10 = 130^\circ \), which is option D. But wait, maybe I made a mistake. Wait, no, let's check the other way. If angle \( TRV \) is \( (2x + 10)^\circ \) and the adjacent angle is \( (x - 10)^\circ \), and they are supplementary. So the calculation is correct.

Wait, no, wait a second. Wait, maybe the angle \( TRV \) is the other angle? Wait, no, the diagram shows that \( T - R - W \) is a straight line, and \( B - R - V \) is a straight line. So angle \( TRV \) and angle \( BR T \) (which is \( (x - 10)^\circ \)) are supplementary? Wait, no, angle \( TRV \) is \( (2x + 10)^\circ \) and angle \( BR T \) is \( (x - 10)^\circ \), and they are supplementary. So when \( x = 60 \), angle \( TRV=2\times60 + 10=130^\circ \), which is one of the options (the last option is \( 130^\circ \)).

Answer:

\( 130^\circ \) (the option with \( 130^\circ \))