Question

the measure of angle b is 83°, and the measure of angle c is 42°. what is the measure of angle d in degrees? 41° 45° 55° 125°

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \( \angle B + \angle C + \angle D = 180^\circ \).

Step2: Substitute known angles

Given \( \angle B = 83^\circ \), \( \angle C = 42^\circ \). Substitute into the formula: \( 83^\circ + 42^\circ + \angle D = 180^\circ \).

Step3: Calculate sum of known angles

\( 83 + 42 = 125 \), so \( 125^\circ + \angle D = 180^\circ \).

Step4: Solve for \( \angle D \)

Subtract \( 125^\circ \) from both sides: \( \angle D = 180^\circ - 125^\circ = 55^\circ \). Wait, no—wait, 180 - 83 - 42: 180 - 83 is 97, 97 - 42 is 55? Wait, no, 83 + 42 is 125, 180 - 125 is 55? Wait, but let me check again. Wait, 83 + 42 is 125, 180 - 125 is 55? Wait, but the options have 55 as an option. Wait, but wait, maybe I made a mistake. Wait, 83 + 42 is 125, 180 - 125 is 55. So angle D is 55 degrees? Wait, but let me recalculate: 83 + 42 = 125. 180 - 125 = 55. Yes. So the measure of angle D is 55 degrees. Wait, but the first option is 41, second 45, third 55, fourth 125. So the correct answer is 55 degrees, which is the third option. Wait, but wait, maybe I messed up the angle labels. Wait, the triangle is labeled B, D, C. So vertices are B, D, C. So angles at B, D, C. So sum is 180. So angle B (at vertex B) is 83, angle C (at vertex C) is 42, so angle D (at vertex D) is 180 - 83 - 42 = 55. Yes. So the answer is 55 degrees, which is the third option (55°). Wait, but let me check again: 83 + 42 = 125. 180 - 125 = 55. Yes. So the measure of angle D is 55 degrees.

Answer:

55° (corresponding to the option with "55°")