\[\text{ We know that the adjacent angles of a parallelogram are supplementry } . \]
\[\text{ Hence }, \left( 3x + 10 \right)° \text{ and } \left( 3x - 4 \right)° \text{ are supplementry } . \]
\[\left( 3x + 10 \right)°+ \left( 3x - 4 \right)° = 180°\]
\[6x° + 6°= 180°\]
\[6x° = 174°\]
\[x = 29°\]
\[\text{ First angle } = \left( 3x + 10 \right)°= \left( 3 \times 29° + 10° \right) = 97°\]
\[\text{ Second angle }= \left( 3x - 4 \right)° = 83°\]
\[\text{ Thus, the angles of the parallelogram are } 97°, 83°, 97° \text{ and } 83°.\]
>
Two adjacent angles of a parallelogram are 3 x 4∘ and 3 x+16∘. Find the value of x and hence find the measure of each of its angles.
Solution
In || gm ABCD, ∠A ∠B are two adjacent angles
Let ∠A=(3x−4)∘ and ∠B=(3x+16)∘
But ∠A+∠B=180∘
⇒(3x−4)∘+(3x+16)=180∘⇒3x−4∘+3x+16=180∘⇒6x+12∘=180∘⇒6x=180∘−12∘⇒6x=168⇒x=1686=28∘∴x=28∘Now ∠A=3x−4=3×28∘−4∘=84∘−4∘=80∘∠B=3x+16=3×28+16=84∘+16∘=100∘But ∠C=∠A opposite angles of||gm∴∠C=80∘Similarly∠D=∠B=100∘Hence∠A=80∘,∠B=100∘,∠C=80∘ and ∠D=100∘
Mathematics
Secondary School Mathematics VIII
Standard VIII
4