In △MNO, m∠M = 78 degrees, m∠N = 34 degrees, and m∠O = 68 degrees In △RST, m∠S = 68 degrees, m∠R = 78 degrees, and m∠T = 34 degrees. describe the pairs of congruent corresponding angles in the two triangles
The pairs of congruent corresponding angles in the two triangles are:
∠M and ∠R (both are 78 degrees)
∠N and ∠T (both are 34 degrees)
∠O and ∠S (both are 68 degrees)
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° ?
The similarity statement that describes the relationship between the two triangles is:
Triangle ABC ~ Triangle 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°
To show the similarity between the two triangles, we need to check if their corresponding angles are congruent.
Triangle ABC: ∠A = 47°, ∠B = 36°, ∠C (unknown)
Triangle GHJ: ∠G = 36°, ∠J = 97°, ∠H (unknown)
To find ∠C (angle in Triangle ABC), we subtract the sum of ∠A and ∠B from 180°:
∠C = 180° - (47° + 36°)
∠C = 180° - 83°
∠C = 97°
Now, we can compare the angles of the two triangles:
∠A = 47° in Triangle ABC
∠G = 36° in Triangle GHJ
∠B = 36° in Triangle ABC
∠H = unknown
∠C = 97° in Triangle ABC
∠J = 97° in Triangle GHJ
The corresponding angles ∠A and ∠G are congruent.
The corresponding angles ∠B and ∠H are congruent.
The corresponding angles ∠C and ∠J are congruent.
Therefore, we can conclude that Triangle ABC ~ Triangle GHJ.
△TUV is isosceles, with ∠T≅∠V and m∠U=54° . What is m∠T ?(1 point) Responses m∠T=126° m angle upper T equals 126 degrees m∠T=63° m angle upper T equals 63 degrees m∠T=54° m angle upper T equals 54 degrees m∠T=36° m angle upper T equals 36 degrees Skip to navigation
Since triangle TUV is isosceles, it means that the angles ∠T and ∠V are congruent. So, if we know that ∠U = 54°, then we can find ∠T.
Since triangles have a sum of angles equal to 180°, we can sum the measures of the angles in triangle TUV:
∠T + ∠U + ∠V = 180°
∠U and ∠V are congruent, so we can rewrite the equation as:
∠T + 54° + ∠T = 180°
2∠T + 54° = 180°
2∠T = 126°
Now we can solve for ∠T:
∠T = 126° / 2
∠T = 63°
Therefore, m∠T = 63°.
△JRW has angle J measuring 47° and angle W measuring 15° . What is the measure of angle R ?
To find the measure of angle R in triangle JRW, we can use the fact that the sum of the angles in a triangle is always 180 degrees.
In triangle JRW, we have:
Angle J = 47°
Angle W = 15°
Angle R = unknown
Sum of angles in triangle JRW: angle J + angle R + angle W = 180°
Substituting the known angle measures:
47° + angle R + 15° = 180°
Combining like terms:
62° + angle R = 180°
To isolate angle R, we subtract 62° from both sides of the equation:
angle R = 180° - 62°
Calculating the value of angle R:
angle R = 118°
Therefore, the measure of angle R in triangle JRW is 118 degrees.