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°?
A. △CAB∼△JHI
B. △BAC∼△HIJ
C. △BCA∼△JIH
D. △ABC∼△HIJ
A. △CAB∼△JHI
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°.
A. △ABC∼△HGJ
B. △ABC∼△HJG
C. △ABC∼△GJH
D. △ABC∼△GHJ
A. △ABC∼△HGJ
△TUV is isosceles, with ∠T≅∠V and m∠U=54° . What is m∠T ?
A. m∠T=126°
B. m∠T=63°
C. m∠T=36°
D. m∠T=54°
Since △TUV is isosceles, we know that ∠T ≅ ∠V. Since the sum of the angles in a triangle is 180°, we can set up the equation: ∠T + ∠U + ∠V = 180°. Substitute the known values: ∠T + 54° + ∠T = 180°. Combine like terms: 2∠T + 54° = 180°. Subtract 54° from both sides: 2∠T = 126°. Divide both sides by 2: ∠T = 63°.
Therefore, the answer is B. m∠T = 63°.
△JRW has angle J measuring 47° and angle W measuring 15°. What is the measure of angle R?
A. m∠R=47°
B. m∠R=28°
C. m∠R=118°
D. m∠R=62°
Since the sum of the angles in a triangle is 180°, we can set up the equation: ∠J + ∠R + ∠W = 180°. Substitute the known values: 47° + ∠R + 15° = 180°. Combine like terms: ∠R + 62° = 180°. Subtract 62° from both sides: ∠R = 118°.
Therefore, the answer is C. m∠R = 118°.