Question

question 15 1 point(s) if m ∠klb = 26 degrees and m ∠blm = 60 degrees. find m ∠klm diagram with l, k, b, m o a) 34 degrees o b) 86 degrees o c) 180 degrees question 16 1 point(s) if m ∠fgb = 105 degrees and m ∠bgh = 54 degrees. find m ∠fgh. diagram with g, f, b, h o a) 51 degrees o b) 159 degrees o c) 180 degrees

Explanation:

Question 15

Step1: Identify angle addition

To find \( m\angle KLM \), we use the angle addition postulate. \( \angle KLM = \angle KLB + \angle BLM \).

Step2: Substitute given values

Given \( m\angle KLB = 26^\circ \) and \( m\angle BLM = 60^\circ \), substitute these into the formula: \( m\angle KLM = 26^\circ + 60^\circ \).

Step3: Calculate the sum

\( 26^\circ + 60^\circ = 86^\circ \).

Step1: Identify angle subtraction (straight line)

Since \( \angle FGH \), \( \angle FGB \), and \( \angle BGH \) are related around point \( G \) with a straight line (implying supplementary angles or angle subtraction for the remaining angle). Wait, actually, looking at the diagram (assuming \( F, G, H \) and \( B \) with \( \angle FGB = 105^\circ \) and \( \angle BGH = 54^\circ \), but actually, if we consider the straight line or the angle around \( G \), wait, no—wait, maybe it's a full angle? Wait, no, the diagram shows \( F \), \( G \), \( H \) with \( H \) downward, \( F \) upward, and \( B \) to the right. So \( \angle FGH \) is the angle between \( FG \) and \( HG \), and \( \angle FGB \) and \( \angle BGH \) are adjacent? Wait, no, maybe it's a linear pair or angle addition. Wait, no—wait, the sum of angles around a point? No, maybe it's a straight line? Wait, no, the problem is to find \( m\angle FGH \) given \( m\angle FGB = 105^\circ \) and \( m\angle BGH = 54^\circ \). Wait, actually, if we consider that \( \angle FGH = \angle FGB + \angle BGH \)? No, that would be more than 180. Wait, no, maybe it's a typo, but looking at the options, 105 + 54 = 159, which is option B. Wait, let's re-examine.

Step1: Angle addition for \( \angle FGH \)

Assuming \( \angle FGH \) is composed of \( \angle FGB \) and \( \angle BGH \) (if the diagram shows \( B \) between \( F \) and \( H \)? No, the diagram shows \( F \) up, \( H \) down, \( B \) right. So maybe \( \angle FGH = \angle FGB + \angle BGH \). Wait, \( 105^\circ + 54^\circ = 159^\circ \), which is option B.

Step2: Calculate the sum

\( m\angle FGH = 105^\circ + 54^\circ = 159^\circ \).

Answer:

B) 86 degrees

Question 16