△LMN is isosceles, with ∠M≅∠L and m∠L=36° . What are the measures of angles M and N ?
Since △LMN is isosceles, we know that ∠M≅∠L.
We are given that m∠L=36°.
Since ∠M≅∠L, we can conclude that m∠M=36° as well.
Since ∠M and ∠N are angles in a triangle, we know that the sum of the angles in a triangle is 180°.
In this case, ∠M + ∠L + ∠N = 180°.
Substituting the given information, we have:
36° + 36° + ∠N = 180°.
Combining like terms, we have:
72° + ∠N = 180°.
Subtracting 72° from both sides, we have:
∠N = 108°.
Therefore, the measures of angles M and N are 36° and 108°, respectively.
In △MNO , m∠M=78° , m∠N=34° , and m∠O=68° . In △RST , m∠S=68° , m∠R=78° , and m∠T=34° . Describe the pairs of congruent corresponding angles in the two triangles.(1 point)
Responses
∠M≅∠S , ∠N≅∠T , ∠O≅∠R
∠M≅∠T , ∠N≅∠R , ∠O≅∠S
∠M≅∠R , ∠N≅∠T , ∠O≅∠S
∠M≅∠R , ∠N≅∠S , ∠O≅∠T
The correct answer is:
∠M≅∠R , ∠N≅∠T , ∠O≅∠S
Which similarity statement describes the relationship between a triangle with angles m∠A=48° , m∠B=17° , and m∠C=115° and another triangle with angles m∠H=17° , m∠I=48° , and m∠J=115° ?(1 point)
△BAC∼△HIJ
△CAB∼△JHI
△BCA∼△JIH
△ABC∼△HIJ
The correct answer is:
△ABC∼△HIJ
Show the similarity between a triangle with angles A , B , and C , where m∠A=47° and m∠B=36° , and another triangle with angles G , H , and J , where m∠G=36° and m∠J=97° .(1 point)
Responses
△ABC∼△HGJ
△ABC∼△GHJ
△ABC∼△HJG
△ABC∼△GJH
The correct answer is:
△ABC∼△GJH
△TUV is isosceles, with ∠T≅∠V and m∠U=54° . What is m∠T ?
m∠T=54°
m∠T=63°
m∠T=36°
m∠T=126°
Since △TUV is isosceles, we know that ∠T≅∠V.
We are given that m∠U=54°.
Since ∠T≅∠V, we can conclude that m∠V=54° as well.
Since ∠T and ∠V are angles in a triangle, we know that the sum of the angles in a triangle is 180°.
In this case, ∠T + ∠U + ∠V = 180°.
Substituting the given information, we have:
∠T + 54° + 54° = 180°.
Combining like terms, we have:
∠T + 108° = 180°.
Subtracting 108° from both sides, we have:
∠T = 72°.
Therefore, m∠T = 72°.