Question

use the figure to complete the statements.
word bank:
36 72 108
blank 1:
blank 2:

Explanation:

Step1: Identify triangle type

The triangle has two equal sides (marked with ticks), so it's isosceles with \( \angle A = \angle C \) or \( \angle A=\angle B \)? Wait, no—equal sides mean opposite angles are equal. So sides \( AB \) and \( BC \)? Wait, no, the marks are on \( AB \) and \( AC \)? Wait, the figure: vertex A, B, C. The two sides with ticks are from A to B? No, looking at the triangle, the two sides with ticks are \( AB \) and \( BC \)? Wait, no, the triangle is labeled A (72°), B, C. The two sides with ticks are \( AC \) and \( BC \)? Wait, no, the marks are on the sides from A to B and from B to C? Wait, no, the standard: in a triangle, equal sides have tick marks. So if two sides are equal, the angles opposite them are equal. So let's see: angle at A is 72°, sides adjacent to B? Wait, maybe the two equal sides are \( AB \) and \( AC \)? No, the tick marks are on the sides from A to B and from B to C? Wait, no, the triangle is drawn with A at the bottom left, B at the top right, C at the bottom right. The two sides with ticks are \( AB \) and \( BC \)? Wait, no, the tick marks are on the sides from A to B and from A to C? Wait, maybe the equal sides are \( AB \) and \( BC \), so angle at A and angle at C are equal? Wait, no, angle opposite equal sides. So if sides \( AB = BC \), then angle at A (72°) and angle at C are equal? Wait, no, angle at A is 72°, side opposite angle B is AC, side opposite angle C is AB. Wait, maybe I got it wrong. Let's recall: in an isosceles triangle, the angles opposite the equal sides are equal. So if two sides are equal, their opposite angles are equal. Let's denote the triangle: vertices A, B, C. Angle at A is 72°. The two sides with ticks: let's say sides \( AB \) and \( AC \) are equal? No, the ticks are on the sides from A to B and from B to C? Wait, the figure shows two sides with ticks: one from A to B, one from B to C? No, maybe the two equal sides are \( AB \) and \( BC \), so angle at A (opposite BC) and angle at C (opposite AB) are equal. So angle A = angle C = 72°. Then angle B = 180 - 72 - 72 = 36°? Wait, but the word bank has 36, 72, 108. Wait, maybe the equal sides are \( AB \) and \( AC \), so angle at B and angle at C are equal. Wait, angle at A is 72°, so angles at B and C: (180 - 72)/2 = 54? No, that's not in the word bank. Wait, maybe I messed up. Wait, the word bank is 36, 72, 108. So let's re-examine. Maybe the two equal sides are \( AB \) and \( BC \), so angle at A (72°) and angle at C are equal, so angle C = 72°, then angle B = 180 - 72 - 72 = 36°. Then maybe the first blank is angle B, which is 36, or angle C? Wait, the problem says "complete the statements" with blanks. Let's assume the first blank is the measure of angle B, the second is angle C or something. Wait, the word bank is 36, 72, 108. So angle at B: 36, angle at C: 72, angle at A:72. So if the first blank is angle B, then 36. Second blank: angle C, 72. Let's check: sum of angles in triangle is 180. 72 + 36 + 72 = 180? No, 72 + 36 + 72 = 180? 72+72=144, 144+36=180. Yes. So angle B is 36°, angle C is 72°. So Blank 1: 36, Blank 2:72.

Step2: Calculate angles

Sum of angles in a triangle: \( 180^\circ \). Let \( \angle A = 72^\circ \), \( \angle B = x \), \( \angle C = y \). If two sides are equal, say \( AB = BC \), then \( \angle A = \angle C = 72^\circ \). Then \( x = 180 - 72 - 72 = 36^\circ \). So \( \angle B = 36^\circ \), \( \angle C = 72^\circ \). So Blank 1 (maybe \( \angle B \)): 36, Blank 2 (maybe \( \angle C \)):72.

Answer:

Blank 1: 36, Blank 2:72 (assuming the blanks are for angle B and angle C, or similar)