*The angles of a triangle are x, y and 40°. The difference between the two angles x and y is 30°. The values of x and y are ……………..*
1️⃣ 45°, 75°
2️⃣ 50°, 80°
3️⃣ 85°, 55°
4️⃣ 55°, 95°
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*The angles of a triangle are x, y and 40°. The difference between the two angles x and y is 30°. The values of x and y are ……………..*
1️⃣ 45°, 75°
2️⃣ 50°, 80°
3️⃣ 85°, 55°
4️⃣ 55°, 95°
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Given :
To Find :
Solution :
Now let the 2 unknown angles be,
☆ As it's mentioned that their is 30
here,
Now let's apply this property and find the angles
[tex] \longrightarrow \sf \: 40 + x + x + 30 = 18 \\ \\ \\ \longrightarrow \sf 70 + 2x = 180 \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \sf \: 2x = 180 - 70 \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \sf 2x = 110 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \sf \: x = \cancel{\frac{110}{2} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \orange{\longrightarrow \bf x = 55 \degree} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
hence the angles are,
● So, option C is correct
Verification :
[tex]\longrightarrow \bf \: 40 + 55 + 85 = 180 \\ \\ \\ \longrightarrow \bf 40 + 140 = 180 \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \bf 180 = 180 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
Left hand side equals Right hand side
[tex] {\huge{ \sf{ \blue{ \underline{ hence \: verified }}}}} {\huge{ \blue{ \dag}}}[/tex]
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[tex]{\large{\underline{\rm{ Properties \:of\:triangles}}}}[/tex]
hope this helps ☆